Enhancing electrical conductivity by defects in metals

Domain: neuroscience
Published: 2026-02-09
Editorial outcome: major_revision

Abstract
High electrical conductivity is crucial for electrics, electronics, communications. Eliminating defects such as grain boundaries and impurities is a primary approach to enhancing electrical conductivity in metals. Although reducing electron-phonon interaction can further contribute to electrical conductivity, only a marginal enhancement is obtained by imposing external pressure even high up to gigapascal. Here we report a contrary strategy to transforming defects into conductive benefits, by forming abundant defects of severely distorted lattice via heterogeneous interface-assisted plastic deformation in metal (copper). Such lattice distortions are generated under a non-extreme condition, and cause internal giant local stress significantly suppressing electron-phonon coupling and thus reducing phonon-caused electron scattering. Consequently, a striking bulk electrical conductivity of >110% IACS is obtained in the copper at room temperature, which is equivalent to the effect of an external high pressure of about 10 gigapascals. Our work provides an extendable approach for developing high-performance metal conductors.

Introduction
Electrical energy is the main form of energy transport and conversion. The development of high-performance conductor materials has the potential to significantly improve the efficiency of systems and devices, reduce energy consumption, and increase integration and power density. Taking an example, the electrical conductivity of interconnects exceeding that of pure copper can effectively improve signal transmission rate, reduce bit error rate, and chip power consumption1–5. According to Matthiessen’s rule, electron scattering caused by phonon and lattice defects, including vacancies, grain boundaries (GBs), impurities, and dislocations, collectively deteriorates electrical conductivity in metals1,6–8. To minimize the deleterious effects of the above electron scattering factors on electrical conductivity, a multitude of methods have been employed, such as increasing lattice integrity and inhibiting grain refinement, as well as purification.

Copper is the most widely used metal conductor material owing to its high conductivity and low cost. However, a very limited increment in the electrical conductivity of Cu has been achieved since the International Annealed Copper Standard (IACS, electrical conductivity of Cu is 100% IACS) was established in 1913. For example, electrical conductivity is less than 103% IACS in oxygen-free Cu with a purity as high as 7N-level, and ~110% IACS in Cu single crystal without GBs9,10. In recent years, some explorations have shown the potential in improving electrical conductivity to a higher level by forming composites either in bulk or on surface2,11–13, and the enhancement of electrical conductivity was mainly attributed to the doping effect, reducing electron scattering on the Cu–C interface, enhancing thermal heat dissipation, etc. But most of the above strategies do not alter the intrinsic electrical conductivity of the metal matrix.

Essentially, the intrinsic electrical conductivity of some phase is dominated by its electronic structure and energy band, which can be influenced by applying external fields, including force, temperature, and magnetism, etc., leading to some strategies such as strain engineering and band engineering14–17. For example, the compression-shear stress on diamond changed charge redistribution and softened phonon, resulting in the production of robust superconductivity18. Regarding metals, it was proved that applying pressure on Cu can suppress electron-phonon coupling (EPC) and thus improve its electrical conductivity, but a very limited increment by 2% was achieved19 when subject to high pressure, even up to 2 gigapascal (GPa). Moreover, in most cases, these benefits are not integrated as intrinsic properties of the materials, and they disappear as the applied fields are removed.

Contrary to the conventional wisdom of eliminating structural defects, we proposed introducing nanolayers of severely distorted copper lattice at GBs in nanograined Cu to act as highly conductive channels by means of suppressing electron-phonon interaction strength and reducing phonon-caused electron scattering. The local giant stress is caused by accumulated copious strain energy upon cold drawing (ε≈12) and subsequent annealing-induced anisotropic expansion due to the thermal expansion coefficient (TEC) mismatch between the Cu matrix and strained graphene at GBs. Additionally, it has high thermal stability (at least up to 773K), and no external extreme fields are required to maintain it.

Results
Fabrication and ultra high electrical conductivity
To obtain sufficient deformability and grain refinement to the nanoscale simultaneously, we incorporated trace graphene (Supplementary Note 1, about several tens of parts per million in volume fraction) at GBs to assist plastic deformation of coarse-grained Cu20. The ultimate nanograined Cu wires were obtained through a sequential process involving in-situ growth of graphene on Cu foils (Supplementary Table 1 and Supplementary Fig. 1), laminated structure assembling, hot-pressing molding, hot extrusion, and cold drawing, followed by a subsequent thermal annealing treatment in the final step (Fig. 1a and Supplementary Fig. 2). Such trace graphene at GBs enables Cu exceptional plastic deformability, i.e. the extruded bar (diameter d=13 mm) can be continuously cold drawn to wires (d<0.03 mm) without intermediate thermal annealing (corresponding to a strain of ~12, Supplementary Figs. 2 and 3). Because of the constraint role of graphene at GBs, Cu samples containing trace graphene (Gr–Cu) have stronger ability on grain refinement and higher thermal stability than that without graphene inside (Fig. 1b, f, Supplementary Fig. 4, and Supplementary Fig. 5). After thermal annealing treatment, with the same diameters (d≈0.4 mm), grain size coarsened up to ~50±13.4 μm in the pure Cu wire (Fig. 1b), much larger than the value of ~0.72±0.21 μm in the Gr–Cu wire (Fig. 1c). As the drawing process continued, nanograined structures were formed and retained in the final cold drawn Gr–Cu wires and annealed Gr–Cu wires, respectively (Supplementary Figs. 11 and 12 and Fig. 1d–f).

We compared the electrical conductivities of Gr–Cu wires and Cu wires prepared using the same raw materials and method (Fig. 1g and Supplementary Fig. 6). For pure Cu wires, as expected, their electrical conductivities decrease gradually with increasing strain, and slightly recover upon thermal annealing treatment. In contrast, the electrical conductivity of the Gr–Cu wires remains almost unchanged in the whole process of cold drawing, and witnessed drastic increases after thermal annealing treatment, with a certified exceptional electrical conductivity larger than 110% IACS (Supplementary Note 2 and Supplementary Fig. 7), which is more than 10% higher than that of pure Cu. It is worth emphasizing that, contradictory to the conventional belief that as the grain size is refined to nanometer scale, the electrical conductivity will significantly decrease21,22, the electrical conductivity inversely increases with decreasing grain size in the plastically deformed Gr–Cu here (Fig. 1h and Supplementary Fig. 8). Our findings strongly suggested that grain refinement not always decreases electrical conductivity, which contradicts the notion established in conventional materials.

While Ag is well known as the best electrical conductor among all the metals, the Gr–Cu here shows comprehensive advantages over Ag as indicated by the expanded area in the performance radar chart (Fig. 1j). Ag has higher electrical conductivity than Cu, but Cu is used in much larger quantities because Ag is too expensive. The Gr–Cu material provides an attractive choice with electrical conductivity higher than Ag but price around Cu. Moreover, pure Cu has a higher current-carrying capacity than Ag, and incorporating graphene will further improve this performance23,24, indicating higher power and safety in applications. Additionally, the density of Gr–Cu is almost the same as that of pure Cu, about 85% that of Ag, implying direct benefit for lightweighting in practical devices and systems. In many applications, high electrical conductivity and high mechanical strength are often required simultaneously, but methods used to strengthen metals generally also cause a pronounced decrease in electrical conductivity1. Fortunately, the Gr–Cu material has both higher electrical conductivity and mechanical strength than either Cu or Ag, which provides a pathway to develop high-performance metal conductors.

Nanostructure formation and lattice distortion
In the as-sintered Gr–Cu sample, a micro-laminated structure was observed, and the lamellae thickness of ~25 μm is close to the thickness of the raw Cu foils and the as-prepared Gr–Cu foils (Supplementary Fig. 9), implying that the inter-lamella graphene inhibited across-lamella grain coarsening in the process of hot-pressing sintering. By subsequent hot extrusion and multi-pass cold drawing, the few-layer graphene at GBs was thinned and further dispersed via shear-induced interlayer sliding (Supplementary Fig. 10 and Supplementary Video 1), and plays the role of inhibiting dynamic recovery and recrystallization against plastic deformation. As a result, the lamellae were continuously thinned and finally refined to the nanoscale (Supplementary Fig. 11).

As the diameter of the Gr–Cu wire reached ~50 μm (corresponding to a strain of ~11), the average lamellar thickness is about 100 nm (Fig. 2a and Supplementary Fig. 11). Such graphene-assisted deformation has a prominent ability for grain refinement, and differs from the conventional refining mechanism dominated by dislocation slip in pure Cu under moderate deformation conditions25,26. The kernel averaged misorientation (KAM) map (Fig. 2b) suggests high misorientation within grains in the as-drawn Gr–Cu wire (d≈50 μm), i.e., a high density of dislocations was accumulated, and copious strain energy was stored inside after cold drawing. Nanotwins are also observed as penetrating through the Cu lamellae with a twin/matrix thickness of ~10 nm (Fig. 2c and Supplementary Fig. 12).

Thermal annealing treatment is the only process resulting in the remarkable enhancement of conductivity, and we compared microstructure change in the annealed Gr–Cu wire (d≈50 μm) (Fig. 2d–g). The nanolaminated structure remained after annealing, and the grains slightly coarsened to an average grain size of 175±138 nm. As a noticeable difference from the as-drawn sample, the annealed sample shows much weaker intragranular misorientation, while strong misorientation concentrates along the lamellar boundary or the Gr–Cu interface (Fig. 2e). These observations imply that the stored strain was redistributed upon thermal annealing. Under high-resolution TEM (HRTEM), we found nanolayers with a clear contrast exist along boundary or interface (Fig. 2f), and corresponding geometrical phase analysis (GPA) shows obvious lattice strain in the nanolayers of Cu matrix (Fig. 2g). Carefully examination of the interplanar spacing of the Cu(111) in the distorted region was changed by ~10% (indicated by the blue and yellow box in Supplementary Fig. 13d).

Furthermore, we estimated the lattice strain by performing synchrotron X-ray micro-diffraction (μ-XRD) (with a wavelength of 0.563 Å and a spot size of ~5 μm) on both the as-drawn and annealed Gr–Cu wire samples (Supplementary Table 2 and Supplementary Fig. 14). The 1-D patterns integrated from the Debye-Scherrer rings27,28 are shown in a 2θ angle range from 10° to 35°. The diffraction peaks at the 2θ angles of 15.5°, 17.9°, 25.5°, 29.9°, and 31.3° correspond to the (111), (200), (220), (311), and (222) planes of Cu, respectively. The as-drawn sample has diffraction peaks with a typical symmetrical profile, indicating homogeneous microstructure and strain distribution (Fig. 2h and Supplementary Fig. 15). Usually, thermal annealing treatment can reduce lattice defects and promote crystallinity, resulting in sharper diffraction peaks29,30. However, some abnormal changes were observed in the μ-XRD patterns of the annealed Gr–Cu sample. After annealing, while the diffraction peak intensities increase significantly, asymmetrical broadening at varying degrees takes place in the peak profiles, typically as shown at the foot of the peaks at low diffraction angles. More μ-XRD patterns with varying features of peak broadening and also some extra peaks are shown in Supplementary Fig. 15. We excluded any possible contribution from impurities to such unusual changes in diffraction patterns because (1) graphene and Cu are immiscible with each other, (2) no oxides were detected by checking peak positions and using electron energy loss spectroscopy. Moreover, the thermal annealing treatment was carried out in an inert atmosphere, and μ-XRD was performed on the polished fresh surface. Hence, we believe that such asymmetrical broadening of peaks was caused by anisotropic strain31 and thus inhomogeneous lattice distortion of the copper lattice in the annealed Gr–Cu wires. Based on the Scherrer equation, we can roughly estimate the type and degree of such observed lattice distortion according to the peak positions, either expansion or compression of interplanar spacing32,33. Lattice compression distortion was mainly reflected by the asymmetrical broadening on the right foot side of some diffraction peaks, with a typical broadening width of about 1~2° for 2θ, indicating that the corresponding interplanar spacing was compressed by ~5% (see Supplementary Note 3 for further details).

Microstructure evolution inducing local strain
To explore the microstructure evolution and formation of lattice distortion during annealing, we conducted in-situ heating experiments in TEM. The low-magnification TEM images revealed that the nanolaminated structure was thermally stable during in-situ heating (Supplementary Fig. 16 and Supplementary Video 2). Closer observations in HRTEM (Fig. 3a–d) show some meaningful details on microstructure evolution. In the randomly selected nanolamella (about 50 nm in width) in the TEM specimen cut from the as-drawn Gr–Cu wire, dense strain moiré fringes were observed in the lamellae before heating34,35. As the heating temperature increased, the strained zone became narrower gradually, and the fringes in the middle region of the nanolamella disappeared ultimately, which seems like the strain was concentrating towards GBs on two sides upon heating. As revealed by HRTEM, two nanolayers with clear contrast and compressive strain (εxy) formed along the GBs on both sides (Supplementary Fig. 17 and Supplementary Video 3), which is consistent with the features of microstructure and nanolayers as observed in the ex-situ annealed Gr–Cu samples (Fig. 2f).

We also conducted Raman measurements of graphene in the interface to estimate the interfacial stress (Fig. 3e). We observed a slight blue shift of the Raman G peak after sintering (without deformation), and a larger shift to higher wavenumbers in the as-extruded Gr–Cu sample (with an extrusion ratio of 9.5 and a strain ε≈2.2). Raman peak position can be used as the index of strain state in graphene; a significant red shift of ~14.2 cm−1 per 1% strain for Raman G peak was observed in graphene under uniaxial tensile strain36. In contrast to the tensile strain, the reported in-plane biaxial compression-induced blue shifts37 of the Raman G peak for the graphite or graphene vary from 4.1 to 4.9 cm−1·GPa−1. Compared to pristine graphene38 or our graphene transferred from Gr/Cu foil to silicon substrate, the blue shift of the Raman G peak in the as-extruded sample is estimated to be around 30 cm−1 in our work. Thus, it can be approximately calculated that the compressive stress caused a shift of the G peak of 6.1–7.3 GPa. It is reasonable to expect that even more significant Raman shifts and thus actual stress much larger than 8 GPa in the annealed Gr–Cu wires (the strain ε as high as 12 in the wire with d<0.03 mm), although it is challenging to further collect Raman spectra for the highly dispersed graphene in the Cu matrix.

This interfacial stress induced by the TEC mismatch between the severely strained graphene and Cu matrix was elucidated in Fig. 3f. Upon elevating temperature during sintering and annealing, along the direction parallel to the nanolamella, graphene contracted due to its negative TEC in-plane39 while the Cu matrix oppositely expanded. Subsequently, graphene tends to expand while Cu tends to shrink, resulting in the formation of graphene wrinkles (described as ripples or folds) during the cooling process. The interfacial compressive stress was partially released by forming folds or ripples40,41, while the majority of the compressive stress was still retained, resulting in a biaxial compressive stress on the Cu matrix. In the other direction, perpendicular to the nanolamella, graphene itself expanded and also constrained the expansion of the Cu matrix, thus leading to a uniaxial compressive stress. Consequently, a multi-directional compressive stress formed near the Cu–C interface, which is consistent with that reported in the graphene/Cu micro-laminated composites42. However, only in the drawn Gr–Cu wire does such a compressive stress effect contribute to a substantial increase in bulk electrical conductivity. Firstly, copious strain energy was accumulated in the process of cold drawing, and graphene was highly strained, resulting in a larger compressive stress generated at the Cu–C interface. Additionally, the proportion of the strain-affected area becomes large enough as the Cu lamellae are refined to the nanoscale. For instance, the width of the distorted nanolayer ranged from 5 to 20 nm for the nanolamellae with a thickness of ~50 nm in Figs. 2f and 3d. Such microstructure evolution and strain accumulation can well explain the strain-dependent enhancement of electrical conductivity (Fig. 1g, h).

Giant stress in the annealed Gr–Cu wire was also confirmed by severe lattice distortion of copper, as shown in the atomic-scale images of the nanolayer (Fig. 3g, h) collected by high-resolution high-angle annular dark-field (HAADF) imaging in an aberration-corrected scanning transmission electron microscope (STEM). As shown in Fig. 3g, we clearly identify a distinctive torsion of the (111) planes. In addition, a typical expansion of (200) interplanar spacing increased by ~27%, from ~1.80 Å to ~2.29 Å in the distorted nanolayer was observed (Fig. 3h and Supplementary Fig. 18), which was confirmed by some extra peaks around 2θ of ~14° in the μ-XRD patterns (inset, Supplementary Fig. 16). Further first-principles calculations indicated that such a large lattice expansion requires local stress of several tens of GPa. We have also conducted molecular dynamics (MD) simulations to elucidate the maintaining effect of graphene on the mechanical properties of the graphene-reinforced copper composites and stable interfacial bonding (Supplementary Fig. 19). The results show the remarkable increase in the tensile strength due to the hindering effect on the dislocations. Especially, comparing with the microstructure at a strain of ~0.5, the microstructure at a strain of ~0.7 was kept stable without interfacial separation. Additionally, the detachment phenomena are less likely to occur under compressive loading43. Thus, based on the above experimental and MD results, interfacial compressive stress was induced and kept without interfacial separation.

Suppression of EPC
Strain-tuning electrically conductive performance was further elucidated by conducting first-principles calculations based on density functional theory (Fig. 4a and Supplementary Fig. 20). The EPC constant λ and Eliashberg spectral function α2F(ω) were obtained. The calculated λ is 0.124 for copper under unstrained conditions. This is in good agreement with the previously reported value41 of 0.14. As the compressive strain increased to 2%, 5%, and 10%, the corresponding calculated λ decreased to 0.113, 0.095, and 0.07, 8 respectively. We also noticed that the spectral functions were shifted to higher frequencies after applying strain, and the intensities of the peaks were reduced, resulting in weakening the scattering effects on electrons. Thus, according to the calculated Eliashberg spectral function α2F(ω) and frequency-dependent EPC λ(ω), we can infer that the electron-phonon interaction strength was reduced after applying strain19,44. As the lattice strain can be determined to be ~5% from the μ-XRD diffraction patterns, a pressure of ~30 GPa was required to achieve a similar lattice strain in the above DFT-calculated hydrostatic pressure. Similar compressive strain increasing the conductivity was also confirmed using experimental tests and simulated calculations in the copper/graphene composites45. Besides, it was recently proposed that the electrical resistivity decreases in aluminum and copper wires upon pressuring each metal19 (Supplementary Fig. 21d). If the graphene-wrapped nanograin in the Supplementary Fig. 21c is analogized to a copper wire, its compressive stress state is similar to that reported in the literature19. Moreover, similar experimental and simulation results on compressive stress suppressing EPC to enhance the conductivity of Au have also been reported in our recent work46. Theory calculations reveal that ~60% increment of electrical conductivity can be achieved at ~30 GPa for the metals of silver and gold47. Göran Grimvall48 systematically investigated the effects of electron-phonon interaction (λ) on the electronic properties and electrical performance, and concluded that λ for the noble metals is well within the approximate limits 0.07–0.24 (Cu), 0.05–0.25 (Ag), and 0.07–0.26 (Au). Besides, a similar recommended value for the Cu, Ag, and Au of ~0.14 was given. Moreover, the ratio of resistivity to temperature (ρ/T) can be used to describe the scattering of conduction electrons by thermal vibrations, and the trend of Cu is close to that of Ag49. As shown in Fig. 2d, 20% nanostructured grains remained in the annealed Gr–Cu wire due to the Cu–C interface. Consequently, we estimated the average electrical conductivity of ~112% IACS according to the rule of mixtures. This is in close agreement with our measurement results of ~110% IACS for the bulk Gr–Cu samples. For comparison purposes, we also accommodated graphene into the DFT model and carried out the corresponding calculations in Supplementary Fig. 22. The calculated λ is 0.171 for the Gr–Cu composite model under unstrained conditions. As the compressive strain increased to 5%, the corresponding calculated λ decreased to 0.137. The variation is about 0.034, which is generally close to that of the FCC copper cell. Considering the distribution of graphene in the Gr–Cu wires and the interfacial compressive stress, graphene was employed as a medium to cause internal giant local stress, resulting in significantly suppressing EPC and enhancing electrical conductivity. Thus, the DFT model of the FCC copper cell could be more suitable to simulate the experimental results.

This suppression of EPC was further confirmed by the measured temperature-dependent resistivity curves of cold-drawn and annealed Gr–Cu composite wires from 3 to 300 K using the physical property measurement system (PPMS) (Fig. 4b). The resistivity of the cold-drawn and annealed Gr–Cu wires at 293 K was 1.67 μΩ·cm and 1.54 μΩ·cm, respectively. This is roughly consistent with the results measured using macroscopic samples in Fig. 1g. As shown in Fig. 4b, the electrical resistivity of the two samples decreased linearly with the temperature down to 100 K. Subsequently, the two curves showed nonlinear trends below 100 K until close to horizontal. It is found that the residual resistivity (ρ0) of the as-drawn sample is 1.75±0.05×10−2 μΩ·cm, which is close to the values (0.51×10−2 μΩ·cm) of the oxygen-free copper (OFC) and the values (0.33×10−2 μΩ·cm) of the single-crystal copper (SCC) in the literature10,21. The residual resistivity values (6.75±0.04×10−2 μΩ·cm) of the annealed sample are larger than those of the as-drawn sample. According to Boltzmann transport theory, the residual resistivity caused by defect scattering is temperature independent50,51. It suggests that the annealed sample contains more defects than that in the cold-drawn sample. Furthermore, the measured temperature coefficient of resistivity at 293 K was ~6.7×10−11 K−1 for the cold-drawn Gr–Cu sample. This matches well with the value of 6.8×10−11 K−1 for the oxygen-free high conductivity (OFHC) Cu52. As a comparison, it was ~5.9×10−11 K−1 for the annealed Gr–Cu sample, which is ~12% lower than that of cold drawn sample. These results indicate that the EPC was suppressed at moderate temperature in the annealed Gr–Cu sample due to the distorted nanolayer.

Our observations indicate that abundant GBs with a distorted lattice in the nanograined Cu enable an exceptional electrical conductivity and also comprehensive properties outperforming those of bulk Ag. Such a property enhancement differs fundamentally from that of the traditional strategies, lying in structural integrity and phase purity. Reduction in the electron–phonon interaction strength by introducing lattice distortion through conventional plastic deformation can be emerged as an intrinsic property of materials, making not only the effect more significant but also extreme external conditions unnecessary, such as high pressure. Our findings also demonstrate that grain refinement (a typical method to enhance strength) does not always lead to a decrease in electrical conductivity, combining strengthening with a second phase (graphene here), which provides an effective approach to enhance electrical conductivity and mechanical strength simultaneously, which has been a long-standing challenge in materials science. Such a strategy, achieving many objectives at one stroke, could also be feasibly applied to many other 2D-material/metal systems, particularly toward the achievement of better performance with superior electrical properties, which are of fundamental and applied importance for advanced engineering applications such as electrical power transport, communication signal transmission, and other electrical systems.

Methods
Materials
The chemical vapor deposition (CVD) process was conducted for graphene growth. Before in-situ grown graphene, in order to remove the surface impurities, the Cu foils with a thickness of 25 μm were immersed in acetone for ultrasonic cleaning. Cold rolled polycrystalline Cu foils with a thickness of ~25 μm and conductivity of ~97.08% IACS were placed in a tube furnace and annealed at 1273 K for 20 min in a hydrogen/argon atmosphere. Subsequently, the methane, which served as the carbon source, was introduced for graphene deposition. The graphene growth was holding on 20 min with methane and hydrogen gasses flow of 3 sccm and 10 sccm, respectively. Then the Gr–Cu foils were rapidly cooled down to room temperature within 30 min. The photograph of Gr–Cu foil, microstructure of Cu matrix and graphene, as well as Raman analysis, are shown in Supplementary Fig. 1. The as-deposited Gr–Cu foils were stacked layer by layer in a graphite die, and the sintering of bulk Gr–Cu composite was carried out using a hot-pressing furnace with a vacuum of ~6×10−2 Pa. The uniaxial pressure of 30 MPa was applied at 400 °C and held for 3 h, followed by continually heating to 900 °C for 2 h, and then naturally cooled down to 100 °C in the furnace.

Hot extrusion was conducted after heating at 750 °C for 40 min. A Φ13 mm bar was obtained, and the surface oxidized layer was removed. Subsequently, the Gr–Cu bar was continually cold-drawn at room temperature. The true strain is defined as ε=ln(A0/A), where A0 and A are the cross-sectional area before and after cold drawing. The whole cold drawing process was carried out at ambient temperature without any intermediate annealing. The annealing process was carried out in a tube furnace at 300–500 °C for 1 h under a tube furnace under a hydrogen/argon atmosphere. The Cu wire was manufactured using the same raw materials and method.

Structure characterization
The sintered sample, different diameter Gr–Cu wires, and annealed Gr–Cu wires were polished. The TEM samples containing the DD and ND cross-sections were prepared by FEI Helios 5CX focus ion beam (FIB). TEM analysis was performed on a FEI Talos F200× at a voltage of 200 keV and a spherical-aberration-corrected TEM (Spectra 300) at a voltage of 300 keV. Electron backscatter diffraction (EBSD) analysis was conducted on a GAIA3 SEM. Transmission Kikuchi diffraction (TKD) was performed on a Mira3 SEM. A nanoMEGAS PED was used to perform the high-resolution grain orientation observation.

Raman characterization
Raman characterization was conducted using a Renishaw inVia Qontor Raman spectroscopy system with a laser wavelength of 532 nm and laser power of 25 W. Calibration with a standard silicon sample was carried out before testing. The spectral resolution was of ≤1.0 cm−1. Further correlative SEM-Raman characterization was carried out on a TESCAN RISE-MAGNA with a laser wavelength of 532 nm.

Mechanical and electrical conductivity testing
The tensile tests of Gr–Cu wires with a diameter of more than 0.5 mm were performed on an Instron 5966 universal testing system with a strain rate of 5×10−4 s−1 at room temperature. A TH-8203S servo control computer tensile testing machine was used for the wires with a diameter of less than 0.5 mm. Five tests were performed to obtain the statistics.

The electrical conductivity tests for wire and foil samples were performed on a test system developed by us based on the Kelvin bridge method (Supplementary Figs. 24 and 25). For the wire sample, a current source meter (Keithley 2601B) was used to provide current, and a nanovoltmeter (Keithley 2182A) was used for measurement of the voltage difference. The diameter of the wire was determined using a laser diameter gauge with an accuracy of ±(0.00012+0.03%D), and we also conducted repeated measurements on a SEM. In addition, a TX-300A resistivity meter was also used to verify the result of the same sample. For the foil sample, a resistivity measurement system based on the van der Pauw method was used (Supplementary Fig. 25). Moreover, known-conductivity pure copper wire (100% IACS) was used for the calibration of the test system.

Synchrotron μ-XRD
In order to examine the lattice strain of the cold-drawn and annealed Gr–Cu wires, the synchrotron μ-XRD experiments were conducted in transmission mode on the BL15U1 beamline of the Shanghai Synchrotron Radiation Facility (SSRF). The main experimental parameters are summarized in Supplementary Table 1. The Gr–Cu wires were thinned using a FIB to enhance the transmission rate. The instrument calibration was performed using a standard CeO2 powder sample. The measured 2D Debye-Scherrer patterns were processed using the Fit2D software28.

In situ TEM shear deformation
TEM sample was prepared in a GAIA3 SEM. The grain boundary, including the Cu–C interface, was determined based on the backscattered image, and a local region containing the Gr–Cu interface was fabricated to ensure the Gr–Cu interface was located in the middle area. The in-situ TEM shear was carried out inside a Titan-ETEM field-emission gun TEM, equipped with an INSTEM S-MT TEM holder under displacement control mode at 2 nm/s. Throughout the shear deformation process. All in situ experiments were recorded in real time by a camera at a shooting interval of ~1 s.

In situ TEM heating testing
In situ TEM heating testing was carried out in a Talos F200X TEM using a FEI heating holder for low-magnification observation and a JEM-ARM300F spherical-aberration-corrected TEM using a DENS solution DH30-4M-JU heating holder for high-magnification microstructure observation. The heating rate was set to 1 K/s with holds at 473 K (15 min), 573 K (15 min), 623 K (15 min), and 673 K (15 min). The temperature measurement of the holder was calibrated by measuring the temperature curve and Raman spectrum of the standard sample. All in-situ heating processes were recorded in real time.

First principles calculations
The first-principles calculations were conducted using the QUANTUM ESPRESSO package53, based on the density functional theory (DFT) with the optimized Norm-Conserving Vanderbilt Pseudopotential54,55. The unit cell of FCC copper was considered using the experimental equilibrium lattice constant of 3.60 Å. The atomic coordinates of the optimized computational models corresponding to the four strain states are provided in the Supplementary Data. The energy cutoff of 100 Ry was chosen for the wavefunctions. The electron charge density was calculated by the Methfessel-Paxton method with a smearing parameter of σ=0.02 Ry (4). To consider the Gr/Cu composite, we constructed the systems by following two steps. Firstly, we relaxed the bulk Cu with fixed different lattice parameters to simulate the effect of a hydrostatic pressure. Then, we cleave the Cu(111) surface to construct the heterojunction of Cu(111)@Gr with two different stacking orders. The heterojunctions are optimized with fixed Cu position and lattice parameters, while the C atoms are fully relaxed. The hydrostatic pressure is simulated by change the crystal parameters and fully relaxed the atomic positions, where the Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton algorithm was used. Phonon dispersion curves were calculated based on the density functional perturbation theory (DFPT)56, where a denser 20×20×20 k-point and a 5×5×5 q-point grids were employed for the EPC calculations. The phonon line width is calculated by
γqv = 2πωqv ∑ij ∫BZ d3k |gqv(k,i,j)|2 × δ(εqv − εF)δ(εk+q,j − εF) (1)
Here, gqv(k,i,j) is the electron-phonon matrix and is defined as
gqv(k,i,j) = ( 2M ℏ ωqv )1/2 ⟨ψi,k | dVSCF / du^qvξ^qv | ψj,k+q ⟩ (2)
where ψ is the wavefunction, V is the Kohn-Sham potential, û is the atomic displacement, and ξ̂ is the phonon eigenvector. The total EPC constant can be evaluated by
λ = ∑qυ λqυ = 2 ∫ α2F(ω) / ω dω (3)
where α2F(ω) is Eliashberg spectral function and is defined as
α2F(ω) = 1 / (2πN(EF)) ∑qυ γqυ / (ℏωqυ) δ(ω − ωqυ) (4)

MD simulations
The MD simulations were performed in the isothermal-isobaric (NPT) ensemble with a constant pressure of 1 atm and temperature maintained at 300 K, utilizing the large-scale atomic/molecular massively parallel simulator (LAMMPS)57. The interatomic interactions in the Cu–C system were modeled using the Embedded Atom Method (EAM) potential for Cu–Cu pairs58, the Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential for C–C interactions59, and the Morse potential for Cu–C pairs43, with a 20 ps NPT ensemble relaxation phase incorporated in the simulation. A polycrystalline composite model was constructed following the multigrain architecture methodology60 proposed by Li et al., with graphene layers embedded at GBs. Periodic boundary conditions were implemented in all spatial dimensions. The simulation employed a timestep of 1 femtosecond (fs) and a strain rate of 5×108 s−1. Atomic configurations were visualized and structurally characterized using the Open Visualization Tool (OVITO)61. The MD trajectories of Cu and Gr–Cu corresponding to the initial and final configurations are provided in the Supplementary Data.

Statistics and reproducibility
Each electrical conductivity value was obtained from three independent samples, and the measurement for each sample was repeated five times. TEM microstructure in Fig. 1f was obtained from the region (marked by a white box) in Fig. 1e, and one experiment was conducted because the regions with similar microstructural characteristics are very common in the EBSD map in Fig. 1e. TEM microstructure analysis in Figs. 2a, d and 3a–d was repeated from three independent samples. Moreover, the typical HRTEM microstructure, such as twins and distorted nanolayer, exists along the boundary or interface, and the distorted lattice was highly reproducible in the three independent experiments.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This paper discussed the improvement in electrical conductivity of copper through the addition of graphene and deformation of composite followed by annealing. It discusses the microstructure of the composite and hypothesizes the mechanisms for enhanced conductivity. While the approach for enhancing conductivity is interesting, I would recommend publication of this paper only after significant information is added on the material and synthesis approach, the measurement approach, material evolution, first principles calculations and clarifying some language concerns.\n1. Pg 2, Ln 33 – 34: Please clarify why an increase of 10% conductivity is equivalent to effect of an external high pressure of about 10 gigapascals – this is not clear anywhere in the paper.\n2. Pg 3, Ln 58 – 61: The authors discuss recent papers where Gr/Cu composites were manufactured showing enhanced electrical conductivity under different conditions, and state that these strategies do not alter intrinsic electrical conductivity of the metal matrix, and still rely on their structural integrity, namely single-crystallization and high purity – which is inherently not true. All the papers reviewed here have added Gr to Cu, meaning they are not relying on single crystallization and high purity. This discussion has to be changed for accuracy.\n3. However, what is more surprising is the authors are doing exactly the same as the papers they cite as ref 11-14 - which is adding Gr to Cu in their study. This leaves the reviewer rather confused because the authors’ premise is to change the intrinsic electrical properties of Cu, but they are doing so by adding Gr(?). The premise (Pg 3, Lines 73 – 76) then seems contradictory and therefore unclear – is the hypothesis to add Gr to Cu so that Gr acts as highly conductive channel? Or is it increasing the defects in Cu alone? And if the measurements are made in the annealed condition, how does that justify the existence of “local giant stresses”? The paper seems to be written for increasing defects in Cu, especially the DFT model, but the results are shown for Gr. Please clarify the hypothesis further.\n4. Pg 3, Line 85: What was the purity of copper and/or alloy composition? What trace elements were present? Since all these components affect conductivity prior to and after straining the composite, it is crucial to present this data.\n5. Pg 3, Line 84 – please provide the graphene content incorporated. This is important information know as the electrical conductivity of a copper/graphene composite is assessed. Studies have shown that conductivity of such composites is a strong function of graphene content.\n6. Pg 5, Line 123: For such a measurement to hold, it is crucial for the authors to discuss the uncertainty in measurement afforded by the system, as well as its calibration of a known-conductivity sample by the system. Given that the authors present conductivity at various sample diameters, uncertainty in measurement for each of these conditions must be presented, along with the temperature of measurement. There are error bars for the conductivity in Fig 1g – are these referring to standard deviation from repeated measurements? What measurement standards were used? What was the gage length used? All these contribute to uncertainty in measurement and need to be discussed. Since the Methods section states that the conductivity tests were performed by the authors on the system they developed (Pg 20, Ln 541), it is not clear what purpose the certification documents in SI are serving – please clarify.\n7. Pg 4, Figure 1g: How was the Cu wire manufactured? Was it made using the same Cu that was used in the synthesis of the Gr-Cu wire? Several details are missing to assess the viability of these results.\n8. Pg 5, Line 124: Pure copper has a range of electrical conductivities depending on its purity – for example, 6N copper is ~103% IACS in electrical conductivity. Thus, it becomes important to discuss the electrical properties of the copper that was used in the study for its relevance to the mechanism.\n9. In all microstructure images, while the scale bars are evident, it is not clear what these bars represent. No text is evident around them to understand what they are – please correct this.\n10. The authors discuss lattice distortion at multiple locations in the paper. Since the material is a composite (Copper and graphene are immiscible as they note in Line 208, Pg 9), then there are two lattices to consider. However, the language in the paper doesn’t specify which lattice is being considered at specific locations. Please clarify this information for further clarity.\n11. There are no images of the graphene species in the extruded or drawn/annealed samples. There is also no discussion of the fate of evolution of the graphene films to whatever becomes of them in the extruded condition. There is an assumption that they become flakes? How and why is not discussed at all. Please provide this information. There is a discussion of ‘nanolayers’ but it is not clear if this refers to graphene or copper. For example, Fig 2f refers to a nanolayer along grain boundary – is this graphene? Is the chemical species carbon? The diffusion region seems like it might be oxide at the interface. Did the authors perform EDS? Significant clarifications are required to reduce confusion in these areas. Similarly, in Fig 3 A-d, it seems like the authors are showing two nanolayers formed along the grain boundaries – are these graphene? The image 3f seems to suggest so, but it is not at all clear either in the caption or in the paper text. Same issue with Fig. 3g and 3h – what layers are being discussed here – what chemical species? All of these chemical species, and material structure needs to be clarified.\n12. Pg 9, Ln 206 – 209: how did the authors exclude any possible contribution from impurities? This is challenging to assess with the information presented here, since no information on the feedstock purity has been provided. Additionally, if the copper and copper/graphene wires were made from foils that were extruded, there should be oxides present significantly, as the lower size of the copper foils without graphene will have a native passivation layer. Was this removed prior to manufacturing the wires? How? Please clarify. Also, unless the extrusion and drawing were performed in a closed environment, the wire will have oxides – please clarify how this is not evident in the results.\n13. If the first principles calculations are comparing an FCC copper cell and another cell, also copper, but with changed crystal parameters and fully relaxed atomic positions (Pg 21, Ln 577 – 583), then yes, the electron-phonon coupling will be lower in cell with relaxed atomic position. But that is not a true representation of the Gr/Cu system whose properties the authors are trying to explain – rather it is only a part of the composite system, the copper part. This therefore cannot be used to explain the conductivity improvements in Gr/Cu composite, as the authors are attempting to do in Pg 13 Ln 325, and in comparison, with Figure 4b with experimental measurements from cold-drawn and annealed Gr-Cu composite system. The DFT model will need to be evolved to accommodate Gr species as well.\n14. The paper discusses only the role of deformation or strain in copper leading to conductivity increase while largely ignoring the role of graphene. There is a growing body of literature that shows that in composites such as those manufactured in this work, the graphene plays an important role in providing high velocity pathways for phonons and electrons. Please interpret your results in that context, since the paper is not discussing the role of graphene beyond pinning grains, which may not sufficiently explain conductivity improvement.\n15. The language in the paper will benefit from grammar and spell check. The issues are too numerous to point out in this review unfortunately but are significant to make it challenging to understand the authors’ arguments at places. Kindly consider editing closely for clarity."}, "author_response": "Response to Reviewers’ Comments\nWe appreciate the reviewers for their valuable comments and professional advice.\nThese opinions are of very helpful for improving academic rigor of our article. Based\non your suggestions and requests, we have made corrections/modifications in the\nrevised manuscript. In the following sections, the reviewers’ comments are in red, and\nour responses to the comments are in black. Based on your suggestions and requests, we have made corrections/modifications in blue in the revised manuscript and\nSupplementary Information. We hope that our work can be improved again.\nFurthermore, we would like to show the details as follows.\nA List of Main Change Made\n1. The expression of “10% conductivity is equivalent to effect of an external high\npressure of about 10 gigapascals” in Abstract has been clarified in Supplementary\nNote 4.\n2. The chemical composition of Cu foils has been supplemented in Supplementary\nTable 1.\n3. The graphene content incorporated have been supplemented in Supplementary\nNote 1.\n4. The detailed analysis and characterization of graphene such as the coverage of\ngraphene on the surface of copper foil and localized SEM-Raman characterization\nhave been supplemented in Supplementary Fig. 1.\n5. The microstructure of graphene in the extruded Gr-Cu samples has been\nsupplemented in Supplementary Fig. 10.\n6. The methods for testing electrical conductivity and the electrical conductivity of\nCu foils have been supplemented in Materials and Methods.\n7. The electrical conductivity of the raw Cu foils and annealed Cu foils have been\nsupplemented in Materials and Methods.\n8. The uncertainty in measurement have been discussed and supplemented in\nSupplementary Note 2.\n9. Molecular dynamics (MD) simulations have been carried out to elucidate the local\ngiant stress was induced and kept without interfacial separation. Relevant results\nhave been revised and supplemented in page 12-13 and Supplementary Fig. 18.\n10. Relevant texts have been supplemented on the scale bars in all the microstructure\nimages.\n11. More detailed clarification of the interfacial compressive stress has been revised\non page 11-12.\n12. DFT model of Gr-Cu composite has been established and the corresponding\ncalculations (0% strained and 5% strained) have been supplemented in\nSupplementary Fig. 20.\n13. Relevant comparative analysis with recent papers has been conducted to evaluate\nthe difference in preparation methods and different mechanism for the conductivity\nimprovement.\n14. The terms of “nanolayer” and “lattice distortion” in the manuscript have been\nclarified in page 8-9.\n15. Other minor revisions of the reviewers have been revised.\nResponses to Reviewers\nReviewer #1 (Remarks to the Author):\nThis paper discussed the improvement in electrical conductivity of copper through the\naddition of graphene and deformation of composite followed by annealing. It discusses\nthe microstructure of the composite and hypothesizes the mechanisms for enhanced\nconductivity. While the approach for enhancing conductivity is interesting, I would\nrecommend publication of this paper only after significant information is added on the\nmaterial and synthesis approach, the measurement approach, material evolution, first\nprinciples calculations and clarifying some language concerns.\nMajor concerns:\nQ1: Pg 2, Ln 33 – 34: Please clarify why an increase of 10% conductivity is equivalent\nto effect of an external high pressure of about 10 gigapascals – this is not clear\nanywhere in the paper.\nR1: Thanks for your suggestion. We interpreted that an external high pressure of about\n10 gigapascals was needed to effect on the bulk copper resulting in an enhancement of\nelectrical conductivity of ~10% IACS (International Annealed Copper Standard, IACS,\nthe electrical conductivity of Cu is 100% IACS) in the Abstract. We clarified the\nreasons as follows:\nAccording to the literature reports1, the electrical conductivity as a function of\npressure for Cu was plotted in Fig. R1a. Linear fitting was performed on the relevant\ndata, and the resistivity ratio is related to the pressure as follows:\ny = −0.01x +1 (1)\nwhere y = ρ/ρ and x = P. Here, ρ is the resistivity under different pressure, ρ is the\n0 0\nresistivity without pressure, P is the pressure. In our present work, an enhancement of\nelectrical conductivity of ~10% IACS means was obtained in the experiments. Thus,\nthe resistivity ratio (ρ/ρ ) can be determined, and the pressure was calculated of ~10\nWe further estimated the external pressure based on the literature reports2 and the\ndensity functional theory (DFT) calculations in our present work. As shown in Fig. R1b,\nwe calculated the electrical phonon coupling parameter (λ) of Cu and plotted the\ncorresponding curve. As comparison, the trend of Cu was similar to the Au, while the\nslope of Cu curve was flatter than Au at the initial stage. The increase of the electrical\nconductivity was determined of ~16% under 10 GPa for the Au in Fig. R1c. Thus, the\nincrease of the electrical conductivity for Cu was estimated of less than 16%, which is\nroughly consistent with the above results, i.e., 10% increase in conductivity is\nreasonable due to the effect of an external high pressure of ~10 GPa.\nRedacted\nFig. R1 | a Variations of resistivity ratio1 (ρ/ρ ), b Electrical phonon coupling parameter2 (λ) and c\n0\nelectrical conductivity2 (1/ρ) with pressure, respectively.\nQ2: Pg 3, Ln 58 – 61: The authors discuss recent papers where Gr/Cu composites were\nmanufactured showing enhanced electrical conductivity under different conditions, and\nstate that these strategies do not alter intrinsic electrical conductivity of the metal\nmatrix, and still rely on their structural integrity, namely single-crystallization and high\npurity – which is inherently not true. All the papers reviewed here have added Gr to Cu,\nmeaning they are not relying on single crystallization and high purity. This discussion\nhas to be changed for accuracy.\nR2: Thank you for your suggestion. We apologize for these ambiguous expressions.\nRelevant reports on the electrical performance of the Gr/Cu composites have\ndemonstrated that the enhancement of electrical conductivity was mainly attributed to\nthe doping effect, reducing electron scattering on the Cu-C interface, enhancing thermal\nheat dissipation, etc. These strategies do not alter intrinsic electrical conductivity of the\nCu matrix, but they have compromised the structural integrity of the metal. Specially,\nsingle-crystallization of the Cu matrix induced by in-situ grown of graphene was\nreported in the literature3. In this case, the increase of electrical conductivity was\nattributed to the single-crystallization of the Cu matrix and doping effect. Relevant\nrevisions have been made on page 3.\nQ3: However, what is more surprising is the authors are doing exactly the same as the\npapers they cite as ref 11-14 - which is adding Gr to Cu in their study. This leaves the\nreviewer rather confused because the authors’ premise is to change the intrinsic\nelectrical properties of Cu, but they are doing so by adding Gr(?). The premise (Pg 3,\nLines 73 – 76) then seems contradictory and therefore unclear – is the hypothesis to\nadd Gr to Cu so that Gr acts as highly conductive channel? Or is it increasing the\ndefects in Cu alone? And if the measurements are made in the annealed condition, how\ndoes that justify the existence of “local giant stresses”? The paper seems to be written\nfor increasing defects in Cu, especially the DFT model, but the results are shown for\nGr. Please clarify the hypothesis further.\nR3: Thank you for your comments. According to the literature reports in references 11-\n14, graphene was in-situ grown on the surface of Cu foil, micro-diameter Cu wire, and\nCu nanowires, respectively. The integrity of graphene was kept unchanged without\nplastic deformation. Thus, the enhancement of electrical conductivity was mainly\nattributed to the doping effect, reducing electron scattering on the Cu-C interface,\nenhancing thermal heat dissipation, etc. Additionally, shear assisted processing and\nextrusion following in-situ grown on the surface of Cu foil was carried out in references\n14.\nDespite the in-situ growth process of graphene on the surface of copper foil was\nsimilar, the Gr-Cu wires in this work were obtained through a sequential process\ninvolving in-situ growth of graphene on Cu foils, laminated structure assembling, hot-\npressing molding, hot extrusion, and cold drawing (Fig. R2). Different from the in-situ\ngrown graphene on the surface of micro-diameter Cu wire, and Cu nanowires, the few-\nlayer graphene at grain boundaries was thinned and further dispersed via shear induced\ninterlayer sliding in this work (Fig. R3 and Supplementary Video 1). The TEM\nobservations of graphene in different conditions were shown in Fig. R3.\nFig. R2 | Schematic illustration of the fabrication process of Gr-Cu wires.\nAs shown in Fig. R3e-h, the few-layer graphene was intensely dispersed along the\ndrawing direction as the plastic strain was increased. Moreover, only a small number of\ncarbon atoms were detected using Electron Energy Loss Spectroscopy (EELS) in the\nlocal region (Fig. R3h). During annealing process, interfacial stress was induced by the\nthermal expansion coefficient (TEC) mismatch between the severely strained graphene\nand Cu matrix. This internal giant local stress significantly suppressing electron-phonon\ncoupling and thus reducing phonon-caused electron scattering. Based on the analysis\nabove, graphene was introduced and dispersed resulting in internal giant local stress,\nFig. R3 | The TEM observations of graphene in different deformed conditions. a HRTEM image of\nCu-C interface of the as-sintered Gr-Cu composite. b The interlayer spacing of graphene marked\nwith red line in (a). c, d HRTEM image of Cu-C interface of the as-extruded Gr-Cu composite and\nthe interlayer spacing of graphene. e, f HRTEM images of Cu-C interface of the cold-drawn Gr-Cu\nwires. g, h Graphene fragments were dispersed in the grain boundaries. i EELS spectra of the\ndispersed graphene in h.\nthus increasing the electrical conductivity of Cu matrix. Graphene served as a medium\nthat provides interfacial stress rather than a highly conductive channel.\nThe existence of local giant stresses in the annealed Gr-Cu wires was justified\nbased on the TEM characterization and synchrotron X-ray micro-diffraction (μ-XRD)\nas well as the measurements of Raman spectra. Under high-resolution TEM (HRTEM),\nwe found nanolayers with a clear contrast exist along boundary or interface (Fig. 2f),\nand corresponding geometrical phase analysis (GPA) shows obvious lattice strain in the\nnanolayers (Fig. 2g). Furthermore, we also conducted in-situ heating experiments in\nTEM, we clearly identify a distinctive torsion of the (111) planes (Fig. 3g) and a typical\nexpansion of (200) interplanar spacing in the distorted nanolayer (Fig. 3h,\nSupplementary Fig. 16). These distorted nanolayer indicated the local giant stresses\nwere formed in the annealed Gr-Cu wires. Further evidence that asymmetrical peak\nbroadening at varying degrees and some extra peaks in the μ-XRD patterns took place\nis demonstrated in Fig. 2h and supplementary Fig. 14. Besides, we also conducted\nRaman measurements of graphene in the interface to estimate the interfacial stress (Fig.\n3e). We observed a larger shift to higher wave numbers in the as-extruded Gr-Cu sample\n(with an extrusion ratio of 9.5 and a strain ε ≈ 2.2). It is reasonable to expect that\neven more significant Raman shifts and thus local giant stresses in the deep cold-drawn\nGr-Cu wires (the strain ε as high as 12 in the wire with d < 0.03 mm).\nIn this work, the term “defect” mentioned in the Abstract refers to the distorted\nlattice of copper caused by the thermal expansion coefficient (TEC) mismatch between\nCu matrix and strained graphene at GBs. Thus, as a medium, graphene was employed\nto cause internal giant local stress significantly suppressing electron-phonon coupling\nand thus enhancing electrical conductivity.\nQ4: Pg 3, Line 85: What was the purity of copper and/or alloy composition? What trace\nelements were present? Since all these components affect conductivity prior to and after\nstraining the composite, it is crucial to present this data.\nR4: Thank you for your suggestion. We totally agree with the reviewer that purity of\ncopper affect conductivity of the composite. The purity of Cu foil used in the in-situ\ngrown graphene is more than 99.99%. The chemical composition analysis results of the\nCu foils using Optical Emission Spectroscopy is displayed in Table R1.\nTable R1 | Chemical composition of Cu foil (wt%).\nCu Pb Fe Sb As P\n≥99.99 ≤0.005 ≤0.005 ≤0.005 ≤0.001 ≤0.001\nQ5: Pg 3, Line 84 – please provide the graphene content incorporated. This is\nimportant information known as the electrical conductivity of a copper/graphene\ncomposite is assessed. Studies have shown that conductivity of such composites is a\nstrong function of graphene content.\nR5: Thank you for your suggestion. We have performed a detailed analysis and\ncharacterization of the graphene on the surface of the copper foil. Random spot\nscanning using Raman microscope (Fig. R4c) and further localized SEM-Raman\ncharacterization (Fig. 4Re-h) demonstrated that different layers graphene was grown on\nthe Cu foil. As shown in Fig. R4b, the proportion of the area covered by graphene is\n~50%. Assuming all the graphene was calculated as three layers, the volume fraction\nof graphene is ~0.004%.\nFig. R4 | Microstructural and Raman characterization of the Gr-Cu foil and graphene. a Electron\nbackscatter diffraction (EBSD) analysis showing Gr-Cu foil exhibits a polycrystalline structure,\nand the average grain size is ~70 μm. b Scanning Electron Microscope (SEM) image of Gr-Cu foil\nshowing the darker graphene covered area. c, d Typical Raman spectra taken from the random\nsampling plots on the surface of the Gr-Cu foil and Raman maps of intensity ratio. e-h Optical\nmicroscope images and the corresponding Raman spot-scanning results.\nQ6: Pg 5, Line 123: For such a measurement to hold, it is crucial for the authors to\ndiscuss the uncertainty in measurement afforded by the system, as well as its calibration\nof a known-conductivity sample by the system. Given that the authors present\nconductivity at various sample diameters, uncertainty in measurement for each of these\nconditions must be presented, along with the temperature of measurement. There are\nerror bars for the conductivity in Fig 1g – are these referring to standard deviation from\nrepeated measurements? What measurement standards were used? What was the gage\nlength used? All these contribute to uncertainty in measurement and need to be\ndiscussed. Since the Methods section states that the conductivity tests were performed\nby the authors on the system they developed (Pg 20, Ln 541), it is not clear what purpose\nthe certification documents in SI are serving – please clarify.\nR6: Thank you for your suggestion. We have summarized the various factors\ncontributing to measurement uncertainty including instrument, test parameter and\nsample parameter in Fig. R5. We first discuss the impact of the measuring instrument\nitself on the measurement results. As described in the Materials and Methods, A current\nsource meter (Kiethley 2601B) was used to provide current, and a nanovoltmeter\n(Kiethley 2182A) was used for measurement of the voltage difference (Fig. R5b). The\ncurrent range that the current source meter can provide is 100 nA to 3 A, and the\nFig. R5 | a Various factors contributing to measurement uncertainty. b Photograph of the\nmeasuring instruments.\nminimum resolution of the nanovoltmeter is 1 nV. The instruments were calibrated\nbefore leaving the factory, which can maintain high sensitivity and accuracy during\ntesting. Moreover, known-conductivity pure copper wire (100%IACS) was used for the\ncalibration of the test system.\nIn addition, the test parameters including test current, ambient temperature and\nnumber of tests can also affect the test results. Firstly, the selection of the test current\nwas determined according to the following procedure: an initial current was used to\nmeasure the resistance. Then we increased the current by 40% and measured the\nresistance again. If the change of the resistance between the two tests exceeded 0.06%\nof the initial resistance, it was considered that the current was too high. In this case, a\nsmaller test current was used and repeated the above steps. For instance, the test current\nof ~5 mA was used for the Gr-Cu wire with diameter of ~50 μm. Besides, a thermometer\nnear the system was used to measure the ambient temperature. And the temperature\ncorrection is carried out as follows:\nR = R\nT 0 1+  ( t t − T ) (2)\nT 0\n0\nwhere R is the resistance at temperature of 20 °C, R is the resistance at temperature\nt\nT\n0\nt,  is the given temperature coefficient at 20 °C, t is the temperature at which\nT\n0\nmeasurement is made, T is 20 °C.\nmeasurement results of the electrical conductivity. The diameter of the wire was\ndetermined using a laser diameter gauge with accuracy of ± (0.00012+0.03%D), and\nthe diameter gauge was calibrated using metal rod with standard dimensions (Fig. R6).\nFig. R6 | a Photograph of a laser diameter gauge. b Metal rod with standard dimensions.\nTo eliminate errors of the diameter measurement duo to the contaminants on the surface\nof the wires, we also conducted repeated measurements on a SEM. Additionally, the\nlengths of the electrode terminals were fixed. The electrode terminals of T and T were\n1 4\nused to provide current, while electrode terminals of T and T were used to measure\n2 3\nthe corresponding voltage. The length between T and T (L ) was 300 mm (Fig. R7).\n2 3 1\nFig. R7 | a Drawings of the DC resistance measurement system. b Photograph of the DC\nresistance measurement system.\nThe error bars for the conductivity in Fig. 1g refer to the standard deviation from\nrepeated measurements. We have supplemented this information in the figure caption.\nDuring the electrical conductivity measurements, the standards of ASTM B193-20 and\nGB/T 351-2019 were used. The gage length for the voltage measurement terminals is\n300 mm (Fig. R7). The electrical conductivity tests were performed on the system\ndeveloped by ourselves. We supplemented the certification documents in\nSupplementary Information to demonstrate the repeatability of our measurement results.\nQ7: Pg 4, Figure 1g: How was the Cu wire manufactured? Was it made using the same\nCu that was used in the synthesis of the Gr-Cu wire? Several details are missing to\nassess the viability of these results.\nR7: Thank you for your suggestion. For comparison, the Cu wire tested in Fig. 1g was\nmanufactured using the same raw materials and method, and these details have been\nsupplemented on page 5 and Materials and Methods.\nQ8: Pg 5, Line 124: Pure copper has a range of electrical conductivities depending on\nits purity – for example, 6N copper is ~103% IACS in electrical conductivity. Thus, it\nbecomes important to discuss the electrical properties of the copper that was used in\nthe study for its relevance to the mechanism.\nR8: Thank you for your suggestion. As described in the manuscript, pure copper has a\nrange of electrical conductivities depending on its purity. As illustrated in Table R1, the\npurity of the Cu foil is ≥99.99%. The electrical conductivity of the as received Cu foil\n(cold rolled state) was 97.08 ± 0.06 %IACS measured using foil sample resistivity\nmeasurement system (Fig. R8). The electrical conductivity of the annealed Cu foil was\n100.18 ± 0.48 %IACS.\nFig. R8 | a Foil sample resistivity measurement system. b Photographs of the meters and sample\nholder.\nQ9: In all microstructure images, while the scale bars are evident, it is not clear what\nthese bars represent. No text is evident around them to understand what they are –\nplease correct this.\nR9: Thank you for your comment. Relevant revisions have been made for all the scale\nbars in all microstructure images.\nQ10: The authors discuss lattice distortion at multiple locations in the paper. Since the\nmaterial is a composite (Copper and graphene are immiscible as they note in Line 208,\nPg 9), then there are two lattices to consider. However, the language in the paper\ndoesn’t specify which lattice is being considered at specific locations. Please clarify\nthis information for further clarity.\nR10: Thank you for your comment. Lattice distortions caused by the thermal expansion\ncoefficient (TEC) mismatch between Cu matrix and strained graphene at GBs were\ndemonstrated using HRTEM characterization in Fig. 2f-g and Fig. 3g-h. And they were\nalso revealed by the asymmetrical broadening in the μ-XRD pattern. These lattice\ndistortions took place in the Cu matrix. As a component of Gr-Cu composite, the\nevolution of graphene during plastic deformation was illustrated in Fig. R3. However,\nit is difficult to observe the lattice of graphene. We have revised this information in\nPage 9 and Page 12.\nQ11: There are no images of the graphene species in the extruded or drawn/annealed\nsamples. There is also no discussion of the fate of evolution of the graphene films to\nwhatever becomes of them in the extruded condition. There is an assumption that they\nbecome flakes? How and why is not discussed at all. Please provide this information.\nThere is a discussion of ‘nanolayers’ but it is not clear if this refers to graphene or\ncopper. For example, Fig 2f refers to a nanolayer along grain boundary – is this\ngraphene? Is the chemical species carbon? The diffusion region seems like it might be\noxide at the interface. Did the authors perform EDS? Significant clarifications are\nrequired to reduce confusion in these areas. Similarly, in Fig 3 A-d, it seems like the\nauthors are showing two nanolayers formed along the grain boundaries – are these\ngraphene? The image 3f seems to suggest so, but it is not at all clear either in the\ncaption or in the paper text. Same issue with Fig. 3g and 3h – what layers are being\ndiscussed here – what chemical species? All of these chemical species, and material\nstructure needs to be clarified.\nR11: Thank you for your question. We have supplemented the microstructure of the\nextruded sample in Fig. R9. As shown in Fig. R9a, different from the lamellar thickness\nof ~25 μm in the as-sintered sample, the thickness of the lamellar was reduced to12-16\nμm after hot extruding. However, the lamellar structure was still preserved in the\nmicrostructure of the extruded sample. We took TEM sample from the grain boundary\nusing focus ion beam (FIB). The wrinkled graphene was clearly observed in the low-\nmagnification image (Fig. R9c). And the multilayers graphene with thickness of 5-10\nnm were observed in the HRTEM image. We also collected the HRTEM images of\ngraphene in the as-sintered, extruded or cold drawn/annealed samples in Fig. R3. The\nfew-layer graphene in grain boundaries was thinned and further dispersed via shear\ninduced interlayer sliding in this work (Fig. R3 and Supplementary Video 1). As shown\nin Fig. R3e-h, the few-layer graphene was dispersed along the drawing direction as the\nplastic strain was increased. Especially, only a small number of carbon atoms were\ndetected using Electron Energy Loss Spectroscopy (EELS) in the deeply deformed Gr-\nCu wire (Fig. R3h).\nFig. R9 | a SEM image of the extruded Gr-Cu composite. b SEM image of the region for TEM\nsample using FIB machining. c, d TEM images of extruded Gr-Cu composite, showing the\nwrinkled graphene was located between the two Cu grains.\nWe found nanolayers with a clear contrast exist along boundary or interface in the\nannealed Gr-Cu wire (Fig. 2f, Fig. R10). In the in-situ heating sample, we also noticed\nthat two nanolayers with clear contrast and compressive strain (ε ) formed along the\nxy\nFig. R3 | The TEM observations of graphene in different deformed conditions. a HRTEM image of\nCu-C interface of the as-sintered Gr-Cu composite. b The interlayer spacing of graphene marked\nwith red line in (a). c, d HRTEM image of Cu-C interface of the as-extruded Gr-Cu composite and\nthe interlayer spacing of graphene. e, f HRTEM images of Cu-C interface of the cold-drawn Gr-Cu\nwires. g, h Graphene fragments were dispersed in the grain boundaries. i EELS spectra of the\ndispersed graphene in h.\nGBs on both sides (Supplementary Fig. 16 and Supplementary Video 3), which is\nconsistent with the features of microstructure and nanolayers as observed in the ex-situ\nannealed Gr-Cu samples. According to the interplanar spacing, this nanolayer was not\ngraphene, and it was distorted Cu matrix.\nFig. R10 | a HRTEM image of the nanolayer in the annealed sample. b Magnification of the\nnanolayer in a. The blue and yellow box showing the distorted lattice.\nThe thickness of the two Cu grains (ex-situ heating and in-situ heating) was less\nthan 100 nm. Thus, we inferred that graphene must exist at the grain boundaries due to\nthe inhibiting effect of graphene on the grain coarsening. It was difficult to observe\natomic-scale image or lattice of the graphene in the deeply drawing sample. And Energy\nDispersive Spectrometer (EDS) could not be used to measure the trace amounts of\ncarbon and oxygen elements. However, we demonstrated the graphene was dispersed\nat the grain boundaries using electron energy-loss spectroscopy (EELS) measurements\non the nanolayer after heating (Fig. R11). As shown in Fig. R10b and d, sharp C-K\nedges peaks were obvious, but no O-K edges peak were observed. Thus, these\nobservations imply that the distorted Cu nanolayer was not oxide.\nBased on the above analysis and the post analysis of the in-situ heating sample\nin Supplementary Information, the nanolayer in Fig. 2f and Fig. 3g, h was distorted Cu\nmatrix.\nFig. R11 | a, b TEM image and EELS spectrum of the in-situ heating sample. c, d TEM image and\nEELS spectrum of the ex-situ heating sample.\nQ12: Pg 9, Ln 206 – 209: how did the authors exclude any possible contribution from\nimpurities? This is challenging to assess with the information presented here, since no\ninformation on the feedstock purity has been provided. Additionally, if the copper and\ncopper/graphene wires were made from foils that were extruded, there should be oxides\npresent significantly, as the lower size of the copper foils without graphene will have a\nnative passivation layer. Was this removed prior to manufacturing the wires? How?\nPlease clarify. Also, unless the extrusion and drawing were performed in a closed\nenvironment, the wire will have oxides – please clarify how this is not evident in the\nresults.\nR12: Thank you for your question. As mentioned in R4, the purity of Cu foil used in\nthe in-situ grown graphene was more than 99.99% (Table R1). The chemical\ncomposition analysis results of the Cu foils using Optical Emission Spectroscopy is\ndisplayed in Table R1. In addition to the copper element, only some trace elements were\ndetected in the Cu foil resulting in the conductivity of 100.18 ± 0.48 %IACS for the\nannealed Cu foil.\nBefore in-situ grown graphene, in order to remove the surface impurities, the Cu\nfoils with a thickness of 25 μm were immersed in the acetone for ultrasonic cleaning.\nThen the Cu foils with a thickness of ~25 μm were placed in a tube furnace and annealed\nat 1273 K for 20 min in hydrogen/argon atmosphere to eliminate the native passivation\nlayer. Moreover, the oxide scale on the surface of the as extruded copper rod was\nremoved using angle grinder before cold drawing. Subsequently, the cold drawn Gr-Cu\nwire was annealed in a tube furnace in hydrogen/argon atmosphere. Relevant revisions\nhave been made on Page 16-17.\nTable R1 | Chemical composition of Cu foil (wt%).\nCu Pb Fe Sb As P\n≥99.99 ≤0.005 ≤0.005 ≤0.005 ≤0.001 ≤0.001\nQ13: If the first principles calculations are comparing an FCC copper cell and another\ncell, also copper, but with changed crystal parameters and fully relaxed atomic\npositions (Pg 21, Ln 577 – 583), then yes, the electron-phonon coupling will be lower\nin cell with relaxed atomic position. But that is not a true representation of the Gr/Cu\nsystem whose properties the authors are trying to explain – rather it is only a part of\nthe composite system, the copper part. This therefore cannot be used to explain the\nconductivity improvements in Gr/Cu composite, as the authors are attempting to do in\nPg 13 Ln 325, and in comparison, with Figure 4b with experimental measurements from\ncold-drawn and annealed Gr-Cu composite system. The DFT model will need to be\nevolved to accommodate Gr species as well.\nR13: Thank you for your suggestion. During cold drawing process, few-layer graphene\nin grain boundaries was thinned and further dispersed via shear induced interlayer\nsliding in this work (Fig. R3 and Supplementary Video 1). As shown in Fig. R3e-h, the\nfew-layer graphene was dispersed along the drawing direction as the plastic strain was\nincreased. During annealing process, giant interfacial stress was induced by the TEC\nmismatch between the severely strained graphene and Cu matrix. The existence of local\ngiant stresses in the annealed Gr-Cu wires has been justified based on the TEM\ncharacterization and synchrotron X-ray micro-diffraction (μ-XRD) as well as the\nmeasurements of Raman spectra. More detailed explanation has been supplemented in\nR3.\nAccording to the graphene evolution and the condition of induced local stress,\nthis dispersed graphene just acted as a medium to provide giant stress, thus suppressing\nelectron-phonon coupling. Compared with the relevant reports in reference 11-13, the\ngraphene in this work possessed different morphology and stress conditions.\nAdditionally, we have accommodated graphene into the DFT model and supplemented\nthe corresponding calculations (0% strained and 5% strained) (Fig. R12).\nFig. R12 | a Side view of Gr-Cu composite model. b Eliashberg spectral function α2F(ω) and\nelectron-phonon coupling λ(ω) for Gr-Cu at different compressive strain of 0% (red) and 5%\n(black).\nAs shown in Fig. R12b, the calculated λ is 0.171 for Gr-Cu composite model under\nunstrained condition. As the compressive strain increased to 5%, the corresponding\ncalculated λ decreased to 0.137. The variation is about 0.034, which is generally close\nto that of the FCC copper cell. Considering the distribution of graphene in the Gr-Cu\nwires and the interfacial compressive stress, graphene was employed as a medium to\ncause internal giant local stress resulting in significantly suppressing electron-phonon\ncoupling and enhancing electrical conductivity. Thus, the DFT model of FCC copper\ncell could be more suitable to simulate the experimental results.\nQ14: The paper discusses only the role of deformation or strain in copper leading to\nconductivity increase while largely ignoring the role of graphene. There is a growing\nbody of literature that shows that in composites such as those manufactured in this work,\nthe graphene plays an important role in providing high velocity pathways for phonons\nand electrons. Please interpret your results in that context, since the paper is not\ndiscussing the role of graphene beyond pinning grains, which may not sufficiently\nexplain conductivity improvement.\nR14: Thank you for your comment. We have collected the TEM images of graphene in\ndifferent samples (Fig. R3). As mentioned in R3 and R11, few-layer graphene in grain\nboundaries was thinned and further dispersed via shear induced interlayer sliding in this\nwork (Fig. R3 and Supplementary Video 1). As the drawing process continued,\nnanograined structures were formed in the deep cold drawn Gr-Cu wires (Fig. R13).\nFig. R13 | a, b SEM images of the cross-sectional microstructure of as sintered and as extruded\nGr-Cu samples. The numbers in the images indicate different lamellar grains. c Band contrast map\nof the cross-sectional microstructure of Gr-Cu wire characterized using PED.\nDuring annealing process, giant interfacial stress was induced by the TEC\nmismatch between the severely strained graphene and Cu matrix. We have clarified the\nexistence of local giant stresses in the annealed Gr-Cu wires based on the TEM\ncharacterization and synchrotron X-ray micro-diffraction (μ-XRD) as well as the\nmeasurements of Raman spectra. Thus, the significant role of graphene can be\nsummarized in the following aspects: 1) refining grains inhibiting grain coarsening; 2)\ninduced giant interfacial stress; 3) reducing temperature coefficient of resistivity.\nAccording to relevant literature reports, the graphene plays an important role in\nproviding high velocity pathways for phonons and electrons. It should be noted that\nthese findings were based on the premise that the structure of graphene was relatively\nintact. Besides, the layers number of graphene has a significant impact on the electrical\nconductivity. However, the graphene in this work was thinned and further dispersed via\nshear induced interlayer sliding during the cold drawing (Fig. R3 and Supplementary\nVideo 1). And it has become almost impossible for graphene to maintain its inherent\nintact structure. Thus, we interpret the high conductivity in this work as due to the giant\ninterfacial stress exerted on the Cu matrix, thus suppressing electron-phonon coupling.\nIn a sense, the influence regions of the interfacial stress in the Cu matrix may also be\nregarded as a “high velocity pathways”. Relevant discussion has been supplemented.\nQ15: The language in the paper will benefit from grammar and spell check. The issues\nare too numerous to point out in this review unfortunately but are significant to make it\nchallenging to understand the authors’ arguments at places. Kindly consider editing\nclosely for clarity.\nR15: Thank you for your suggestion. We apologize for the grammar and spell issues.\nCareful and comprehensive revision has been made in the revised manuscript.\nReviewer #2:\nThe submitted manuscript is improving electrical conductivity of copper by introducing\nseverely distorted lattice via so-called heterogeneous interface assisted plastic\ndeformation. To achieve such lattice distortions, the authors utilized graphene/copper\ncomposites, prepared via CVD on Cu foil followed by hot pressing, hot extrusion, cold\ndrawing, and annealing, with >100% IACS. Based on their analysis, the conductivity\nimprovement is equivalent to 10 GPa. The topic is very interesting and relevant to the\nreaders of Nature Communications. However, the reviewer has several concerns about\ntheir analyses and claims, including the major and minor comments listed below.\nConsidering the high standard of Nature Communications, the current manuscript\nrequires major corrections and clarifications.\nMajor comments\nQ1: The importance of the multi-layer graphene for the Cu plastic deformation was\nemphasized, for example, on page 6, line 151 “the fewer-layer graphene at GBs was\nthinned and further dispersed via shear induced interlayer sliding …”. Graphene from\nthe supplementary video and all the highresolution TEM images is multi-layer; while\nall the Raman spectra (Figure3e, Supplementary Fig.1) of as-synthesized graphene\nshows mono- or bi-layer graphene (I /I ratio >1). Please explain this discrepancy.\n2D G\nR1: Thank you for your suggestion. We have performed a detailed analysis and\ncharacterization of the graphene on the surface of the copper foil. The Raman spectra\n(Fig. 3e and Supplementary Fig.1) of as-synthesized graphene showing mono- or bi-\nlayer graphene (I /I ratio >1) was obtained with random spot scanning using a\n2D G\nRenishaw inVia Qontor Raman spectroscopy system. Further localized SEM-Raman\ncharacterization (Fig. R4e-h) using a TESCAN RISE-MAGNA demonstrated that\ngraphene with different layers was grown on the Cu foil. For instance, the Raman\nspectra of P3, P4 and P5 shows different I /I ratio. These observations imply that\n2D G\nmono- or bi-layer graphene, few-layer graphene and even multilayer graphene coexist\non the Cu foil.\nSimilar to the FIB machining for the extruded sample in Fig. R9, the more clearly\nvisible grain boundary (R1 region) was selected for the TEM sample in the as sintered\nGr-Cu sample. Moreover, compared to monolayer graphene, multilayer graphene was\neasier to be detected. Thus, multilayer graphene was observed in the TEM images.\nFig. R4 | Microstructural and Raman characterization of the Gr-Cu foil and graphene. a Electron\nbackscatter diffraction (EBSD) analysis showing Gr-Cu foil exhibits a polycrystalline structure,\nand the average grain size is ~70 μm. b Scanning Electron Microscope (SEM) image of Gr-Cu foil\nshowing the darker graphene covered area. c, d Typical Raman spectra taken from the random\nsampling plots on the surface of the Gr-Cu foil and Raman maps of intensity ratio. e-h Optical\nmicroscope images and the corresponding Raman spot-scanning results.\nFig. R9 | a SEM image of the extruded Gr-Cu composite. b SEM image of the region for TEM\nsample using FIB machining. c, d TEM images of extruded Gr-Cu composite, showing the\nwrinkled graphene was located between the two Cu grains.\nQ2: On page 9, the authors wrote “shows some meaningful details on microstructure\nevolution. In the randomly selected nanolamella (about 50 nm in width) in the TEM”.\nHowever, the total account of available graphene is very limited (to be specific, mono-\nor bi-layer graphene (based Raman in Figure 3e) on 25-um copper). Imagine that the\nmono- or bi-layer graphene is distributed along ~175nm thick laminar grain structures\nwithin 25-um thick copper. Clearly, the account of graphene at Cu grains will be very\nlimited, which is true even if multilayer graphene is assumed. Can the authors explain\nhow such a small amount of graphene can cause and maintain such large internal stress\n(~10 GPa). Furthermore, why don’t Cu go through plastic deformation to relax the\ninternal stress? Lastly, Cu-Gr surface energy is very weak. Can you explain how such\nlarge internal stress does not cause interfacial separation?\nR2: Thank you for your question. Further localized SEM-Raman characterization in\nFig. R4e-h demonstrated that mono- or bi-layer graphene, few-layer graphene and even\nmultilayer graphene coexist on the Cu foil. Assuming all the graphene was calculated\nas calculated\nas three layers, the volume fraction of graphene was determined of ~0.004%.\nThe graphene in this work was thinned and further dispersed via shear induced\ninterlayer sliding during the cold drawing. During annealing process, giant interfacial\nstress was induced by the thermal expansion coefficient (TEC) mismatch between the\nseverely strained graphene and Cu matrix. We have demonstrated the existence of local\ngiant stresses in the annealed Gr-Cu wires based on the lattice distortion, asymmetrical\nbroadening of synchrotron X-ray micro-diffraction (μ-XRD) peaks and Raman peak\nshift using TEM characterization, μ-XRD and measurements of Raman spectra,\nrespectively. Furthermore, it was recently proposed that the instantaneous peak thermal\nstress on the Cu-C interface could exceeds 10 TPa for an 800 °C temperature gradient\ndue to the TEC mismatch4.\nWe have also supplemented molecular dynamics (MD) simulations to elucidate\nthe maintaining effect of graphene on the mechanical properties of the graphene-\nreinforced copper composites (Fig. R14). The results show the remarkable increase in\nthe tensile strength due to the hindering effect on the dislocations. Especially,\ncomparing with the microstructure at strain of ~ 0.5, the microstructure at strain of ~\n0.7 was kept stable without interfacial separation. This observation suggests that the\ngraphene could maintain the stress and interfacial bonding.\nThe Morse potential function for Cu-C interactions in graphene-reinforced\nFig. R14 | Atomic configurations from MD simulation of Gr-Cu composite and Cu under tensile\nloading using Morse potential. a-c Gr-Cu composite. d, e Pure Cu. f Tensile stress-strain curves.\ncomposites, adapted from Mustapha Makan et al.5, demonstrates superior binding\nenergy compared to conventional Lennard-Jones potentials6. During the MD\nsimulations in Fig. R14, Morse potential was selected to describe Cu-C interactions.\nThe Cu-C interface was kept unseparated under stress. We also conducted the\nsimulations using the Lennard-Jones (LJ) potential in Fig. R15. Compared with the\nresults using Morse potential in Fig. R14, interfacial separation of Cu-C was observed\nin Fig. R15. According to the literature reports, MD simulations using the Lennard-\nJones (LJ) potential demonstrated that the detachment of the Ni-C interface was\nobserved, and such detachment phenomena are less likely to occur under compressive\nloading5. These simulations hints that the LJ potential does not adequately capture the\ninterfacial bonding strength. Thus, based on the above experimental and MD results,\ninterfacial compressive stress was induced and kept without interfacial separation in\nthis work.\nFig. R15 | Atomic configurations from MD simulation of Gr-Cu composite under tensile loading\nusing LJ potential, showing interfacial separation of Cu-C.\nQ3: The electrical conductivity of Gr-Cu composites is determined by multiple factors.\nExcept for the lattice distortion due to large pressure, at least two more factors need to\nbe considered: (1) the average lamellar thickness of Cu is about 100 nm (page 8, line\n171) and 175 nm (after annealing, page 8, line 184), which is comparable to the\nelectron mean-free path of Cu (~40 nm). Therefore, surface scattering within each Cu\nlamellar could be significant, may result an increase in electrical resistivity of up to 8-\n15% (Fuchs-Sondereimer model). (2) The graphene as reinforcement is severely\ndamaged after sintering and extrusion (Figure 3e, large D peak, disappear of 2D peak),\nit may behave as impurity within Cu matrix to hinder the electron transport\n(Matthiessen’s rule). Please explain why the ~10% improvement is solely from pressure\neffect and all other factors are negligible.\nR3: Thank you for your comments. Considering the quantum effect of the free electrons,\nFuchs and Sondheimer proposed a theoretical model (F-S model) to describe the\nvariation of electrical resistivity of metal thin films with thickness. According to the F-\nS model, the resistivity increases with decreasing the film thickness7. We also noticed\nsome literatures on the electrical properties and the film thickness of Cu films8,9.\nRedacted\nFig. R16 Variation of resistivity with thickness for Cu thin films 8.\nAs the thickness of metal films decrease into nanoscale and even is comparable\nwith mean free path of electrons, surface scattering has a significant impact on the\nelectrical resistivity. However, as shown in Fig. R16a, the electrical resistivity of Cu\nfilms is close to the bulk state value (1.67 μΩcm) at approximately 160 nm thickness8.\nMoreover, statistical results showed that the fraction of twin boundaries (TBs) in the\ncold drawn Gr-Cu sample was 11% (Fig. R15). High density TBs has lower electrical\nresistivity. Based on above analysis, the factor of surface scattering is negligible.\nThe localized SEM-Raman characterization was shown in Fig. R4. Assuming all\nthe graphene was calculated as three layers, the volume fraction of graphene was\ndetermined of ~0.004%. Additionally, most of the graphene was thinned in nanoscale\nand dispersed in the grain boundaries. By considering from the perspective of impurities,\nthis low content of graphene has almost no effect on the resistivity.\nWe also noticed that one-to-two layers graphene with intact structure may provide\nhigh-velocity pathways for the electron mobility. However, the few-layer graphene in\ngrain boundaries was thinned and further dispersed via shear induced interlayer sliding\nin this work (Fig. R3 and Supplementary Video 1). As shown in Fig. R3e-h, the few-\nFig. R3 | The TEM observations of graphene in different deformed conditions. a HRTEM image of\nCu-C interface of the as-sintered Gr-Cu composite. b The interlayer spacing of graphene marked\nwith red line in (a). c, d HRTEM image of Cu-C interface of the as-extruded Gr-Cu composite and\nthe interlayer spacing of graphene. e, f HRTEM images of Cu-C interface of the cold-drawn Gr-Cu\nwires. g, h Graphene fragments were dispersed in the grain boundaries. i EELS spectra of the\ndispersed graphene in h.\nlayer graphene was dispersed along the drawing direction as the plastic strain was\nincreased. Especially, only a small number of carbon atoms were detected using\nElectron Energy Loss Spectroscopy (EELS) in the deeply deformed Gr-Cu wire (Fig.\nR3h). Based on previous studies and our present experimental results, we attributed the\n~10% improvement of conductivity to the pressure effect.\nQ4: On page 13, line 307-311, the logical reasoning in this section to estimate the\nimprovement ofelectrical conductivity of Cu is weak. (1) Why “~30 GPa gives 60%\nimprovement of electrical conductivity for Ag and Au” is applicable for Cu? (2) How\ndoes “~20% nanostructured grains remain after annealing” result in 112% IACS in Cu?\nPlease give more logical reasoning details.\nR4: Thank you for your question. As demonstrated in Matthiessen’s rule, the total\nresistivity is the sum of contributions from the electrons scattering by the lattice\nvibrations (ρ ) and lattice defects scattering. Göran Grimvall systematically\nel-ph\ninvestigated the effects of electron-phonon interaction (λ) on the electronic properties\nand electrical performance10, and concluded that λ for the noble metals is well within\nthe approximate limits 0.07-0.24 (Cu), 0.05-0.25 (Ag) and 0.07-0.26 (Au). Besides,\nsimilar recommended value for the Cu, Ag and Au of ~0.14 was given. Moreover, ρ/T\ncan be used to describe the scattering of conduction electrons by thermal vibrations.\nAs shown in Fig. R17, the trend of Cu is close to that of Ag. Theory calculations reveals\nthat ~60% increment of electrical conductivity can be achieved at ~30 GPa for the\nmetals of silver and gold. Thus, it is reasonable to roughly estimate the pressure effects\non the conductivity of Cu.\nRedacted\nFig. R17 | a The ratio ρel-ph(T)/T for Cu and Ag10. b Electrical conductivities2 as a function of\napplied hydrostatic pressures at 300 K.\nAs the lattice strain can be determined of ~5% from the μ-XRD diffraction patterns,\n~30 GPa interfacial stress was induced in the Cu-C interface resulting in ~60%\nincrement of electrical conductivity, i, e., ~160 %IACS was achieve in the partial area\nwhere graphene was distributed. According to the Precession electron diffraction (PED)\ndata of the annealed sample, ~20% nanostructured grains were remained after annealing.\nThus, we can approximately estimate that the proportion of areas containing graphene\nof ~20%. The conductivity of 112%IACS was roughly calculated according to the rule\nof mixtures as follows:\n20%160%IACS +80%100%IACS =112%IACS (2)\nQ5: On page 11, line 263-272, the compressive stress due to thermal mismatch between\ngraphene and copper upon elevating temperature was given. However, annealing and\nsintering is always followed by cooling process. On the contrary, because of the thermal\nmismatch in thermal expansion coefficient, during the cooling process, graphene tends\nto expand while Cu tends to shrink. And this is the reason for the formation of graphene\nwrinkles. As a result, in contrast to compressive stress, tensile stress is more likely after\ncooling down from the annealing and sintering. Please explain this discrepancy.\nR5: Thank you for your question. We totally agree with the reviewer that graphene\ntends to expand while Cu tends to shrink resulting in the formation of graphene wrinkles\nduring the cooling process. These wrinkles can be described as ripples or folds.\nHowever, according to most of the literature reports, the compressive stress was formed\nduring the cooling11,12. As shown in Fig. R18, the interfacial compressive stress was\npartially released by forming folds or ripples, while the majority of the compressive\nstress was still retained. This interfacial compressive stress manifests as a blueshift in\nFig. R18 | Schematic of possible mechanism of fold11.\nthe Raman spectrum. Furthermore, in-situ observation of wrinkling phenomenon13 was\nconducted to demonstrate the compressive stress in the epitaxial graphene grown on\nPt(111) and Ir(111).\nBased on above analysis and the Raman spectrum in Fig. 3e, we interpret the\nformed stress as compressive stress due to the thermal mismatch between graphene and\ncopper during the cooling process. Relevant revisions have been made on page 11-13.\nQ6: Please cite the references correctly. For example: (1) reference [2] and [12] are\nthe same; (2) on page 2, reference [9] and [10] reported the electrical conductivity of\nsingle crystal Cu without grain boundaries (GBs) to be higher than 110% IACS, not\n105% mentioned in this work; (3) on page 5, line 126, “ electrical conductivity is\nproportional to grain size …” neither [22] or [23] gives this conclusion; (4) [23] was\npublished in 1969, not 2009; etc.\nR6: Thank you for your comments. We apologize for these issues in the references.\nRelevant revisions have been made in the revised manuscript.\nMinor comments\nQ1: Please give calculation details. For example, on page 9, line 213-218, the\ninterplanar spacing is calculated based on the Scherrer equation without details.\nPlease also provide details of the calculations for the other major quantitative analysis.\nR1: Thank you for your suggestion. We have supplemented relevant details for the\nmajor quantitative analysis as follows:\n1) The content of graphene on the Gr-Cu foils\nRandom spot scanning using Raman microscope (Fig. R4c) and further localized\nSEM-Raman characterization (Fig. Re-h) demonstrated that different layers graphene\nwas grown on the Cu foil. As shown in Fig. R4b, the proportion of the area covered by\ngraphene is ~50%. Assuming all the graphene was calculated as three layers, the\nvolume fraction of graphene is ~0.004%.\nFig. R4 | Microstructural and Raman characterization of the Gr-Cu foil and graphene. a\nElectron backscatter diffraction (EBSD) analysis showing Gr-Cu foil exhibits a polycrystalline\nstructure, and the average grain size is ~70 μm. b Scanning Electron Microscope (SEM) image of\nGr-Cu foil showing the darker graphene covered area. c, d Typical Raman spectra taken from the\nrandom sampling plots on the surface of the Gr-Cu foil and Raman maps of intensity ratio. e-h\nOptical microscope images and the corresponding Raman spot-scanning results.\n2) Interplanar spacing of the distorted lattice\nThe Scherrer Equation and Bragg’s Law are often used to estimate the crystallite\nsize and lattice strain conditions. The asymmetrical broadening of about 1~2° for 2θ was\nobserved in Fig. S14. In view of the average deviations of the (111) peak position from\nthe standard value, we can roughly estimate mean variation of interplanar spacing (d )\n111\naccording to the Bragg’s Law (  = 2d sin ). The lattice strain can be roughly estimated\nof ~5% according to the formula of  = d / d .\n0\n3) ~20% nanostructured grains remained after annealing resulting in 112%\nIACS in Cu\nAs demonstrated in Matthiessen’s rule, the total resistivity is the sum of\ncontributions from the electrons scattering by the lattice vibrations (ρel-ph) and lattice\ndefects scattering. Göran Grimvall systematically investigated the effects of electron-\nphonon interaction (λ) on the electronic properties and electrical performance, and\nconcluded that λ for the noble metals is well within the approximate limits 0.07-0.24\n(Cu), 0.05-0.25 (Ag) and 0.07-0.26 (Au). Besides, similar recommended value for the\nCu, Ag and Au of ~0.14 was given10. Moreover, ρ/T can be used to describe the\nscattering of conduction electrons by thermal vibrations. As shown in Fig. R17, the\ntrend of Cu is close to that of Ag. Theory calculations reveals that ~60% increment of\nelectrical conductivity can be achieved at ~30 GPa for the metals of silver and gold.\nThus, it is reasonable to roughly estimate the pressure effects on the conductivity of Cu.\nFig. R17 | The ratio ρel-ph(T)/T for Cu and Ag10. b Electrical conductivities2 as a function of\napplied hydrostatic pressures at 300 K.\nAs the lattice strain can be determined of ~5% from the μ-XRD diffraction patterns,\n~30 GPa interfacial stress was induced in the Cu-C interface resulting in ~60%\nincrement of electrical conductivity, i, e., ~160 %IACS was achieve in the partial area\nwhere graphene was distributed. According to the Precession electron diffraction (PED)\ndata of the annealed sample, ~20% nanostructured grains were remained after annealing.\nThus, we can approximately estimate that the proportion of areas containing graphene\nof ~20%. The conductivity of 112%IACS was roughly calculated according to the rule\nof mixtures as follows:\n20%160%IACS +80%100%IACS =112%IACS (3)\nQ2: Please be careful about the calculations. For example: (1) on page 11, line 253-\n258, the reported blue shift (from 4.1-4.9 cm-1GPa-1) and the blue shift from this work\n(~30 cm-1) gives a compressive stress of 6.1-7.3 GPa, not ~8 GPa; (2) on page 12, line\n286-287 and also Figure 3h, the interplanar spacing of Cu(100) is not 1.8Å but 3.6 Å.\nR2: Thank you for your comments. We apologize for these issues in the manuscript.\nAccording to the extinction rules of the face-centered cubic structure, the (100) plane\nwill undergo systematic extinction in the X-ray diffraction (Fig. R19). The interplanar\nspacing of Cu (200) plane is 1.8Å. Relevant revisions have been made in the revised\nmanuscript.\nFig. R19 | Diffraction pattern of copper taken along [110] zone axis.\nQ3: On page 5, the authors claimed that “As the drawing process continued,\nnanograined structures were formed in the final deep cold drawn Gr-Cu wires (Fig. 1,\nD to F).” However, Figure 1e shows mainly microscale grains. Please provide an\nexplanation.\nR3: Thank you for your comments. We have characterized the microstructural\nevolution in Fig. R20. As the drawing process continued, nanograined structures were\nFig. R20 | Microstructure and grain size of the cold-drawn samples. a-c Typical DD-ND cross-\nsectional; d-g TD-ND cross-sectional IPF maps of cold drawn samples with different diameter. h\nGrain size distribution of cold drawn Gr-Cu wire with diameter of ~0.05 mm. i Variations of\nmeasured grain size with the diameter of Gr-Cu wires.\nformed in the final deep cold drawn Gr-Cu wires (Fig. S12). Fig. 1d-f show the EBSD\nmaps and TEM image of annealed Gr-Cu wires with different diameter. We apologize\nfor this incorrect note in the manuscript. Relevant revisions have been made in the\nrevised manuscript.\nQ4: From XRD and blue shift of Raman peak, the super-large compressive stress on Cu\n(therefore smaller inter-planar spacing) was confirmed. However, on page 12, line 285-\n290, the highlighted evidence for lattice distortion (i.e., Figure 3H) emphasized the\nlarge increase in (~27%) interplanner spacing. Please explain the discrepancy.\nR4: Thank you for your question. We have demonstrated the existence of local giant\nstresses in the annealed Gr-Cu wires based on the asymmetrical broadening of\nsynchrotron X-ray micro-diffraction (μ-XRD) peaks and Raman peak shift using μ-\nXRD and measurements of Raman spectra, respectively. Additionally, lattice expansion\nof ~27% for the (200) plane was demonstrated in Fig. 3h. As shown in Fig. R21, the\ndirection of the compressive stress was nearly vertically downward, thus leading to the\nlocal lattice expansion of (200) plane.\nFig. R21 | Microstructure and grain size of the cold-drawn samples.\nQ5: Supplementary Fig.1d shows a polycrystalline Gr-Cu foil. It was previously\nreported by the author’s group that after CVD, a strong Cu(111) was detected and\naccompanied by a significant grain coursing. Please explain this discrepancy.\nR5: Thank you for your question. We interpreted this discrepancy as follows:\nDifferent Cu foils were employed for the graphene growing in this work comparing\nwith our previous work (Cao, M., Xiong, D. B., Yang, L. et al., Ultrahigh electrical\nconductivity of graphene embedded in metals. Adv. Funct. Mater. 29, 1806792 (2019)).\nFurthermore, larger quantities and larger area of single piece of Cu foils were\nsimultaneously placed in the furnace for in-situ growth of graphene, i.e., similar to\nindustrial-scale methods. Thus, the differences in the raw materials and processes\nmentioned above may results in different microstructures of the Gr-Cu foils.\nReferences\n1. Lanzillo, N. A., Thomas, J. B., Watson, B., Washington, M., Nayak, S. K.\nPressure-enabled phonon engineering in metals. Proc. Natl. Acad, Sci. 111, 8712-\n8716 (2014).\n2. Giri, A., Gaskins, J. T., Li, L., Wang, Y. S., Prezhdo, O. V., Hopkins, P. E. First-\nprinciples determination of the ultrahigh electrical and thermal conductivity in\nfree-electron metals via pressure tuning the electron-phonon coupling factor. Phys.\nRev. B 99, 165139 (2019).\n3. Cao, M., Xiong, D. B., Yang, L., Li, S. S., Xie, Y., Guo, Q., Li, Z., Adams, H., Gu,\nJ., Fan, T., Zhang, X., Zhang, D. Ultrahigh electrical conductivity of graphene\nembedded in metals. Adv. Funct. Mater. 29, 1806792 (2019).\n4. Zhang, X., Xu, Y., Wang, M., Liu, E., Zhao, N., Shi, C., Lin, D., Zhu, F., He, C.\nA powder-metallurgy-based strategy toward threedimensional graphene-like\nnetwork for reinforcing copper matrix composites. Nat. Comm. 11, 2775 (2020).\n5. Makan, M., Makan, A., Ghoulbzouri, A.E. Effect of graphene network\nreinforcement and interface orientation on the mechanical behavior of nickel\ncomposites: A molecular dynamics study. Acta Mater. 284, 120637 (2025).\n6. Duan, K., Zhu, F., Tang, K., He, L., Chen, Y., Liu, S. Effects of chirality and\nnumber of graphene layers on the mechanical properties of graphene-embedded\ncopper nanocomposites. Comput. Mater. Sci. 117, 294-299 (2016).\n7. Camacho, J.M., Oliva, A.I. Surface and grain boundary contributions in the\nelectrical resistivity of metallic nanofilms. Thin Solid Films. 515, 1881-1885\n(2006).\n8. Khojier, K., Savaloni, H. A study on the dependence of DC electrical properties\nand nanostructure of Cu thin films on film thickness. Int. J. Nano Dimens. 3, 217-\n226 (2013).\n9. Wang, M., Zhang, B., Zhang, G.P., Yu, Q.Y., Liu, C.S. Effects of interface and\ngrain boundary on the electrical resistivity of Cu/Ta multilayers. J. Mater. Sci.\nTechnol. 25, 699-702 (2009).\n10. Grimvall, G. Many-body corrections to the effective electron mass in the noble\nmetals. Phys. Kondens. Materie. 11, 279-285 (1970).\n11. Wang, M., Huang, M., Luo, D., Li, Y., Choe, M., Seong, W.K., et al. Single-crystal,\nlarge-area, fold-free monolayer graphene. Nature. 596, 519-524 (2021).\n12. Hattab, H., N’Diaye, A.T., Wall, D., Klein, C., Jnawali, G., Coraux, J., et al.\nInterplay of wrinkles, strain, and lattice parameter in graphene on Iridium. Nano\nLetters. 12, 678-682 (2012).\n13. N’Diaye, A.T., Gastel, R., Martínez-Galera, A.J., Hattab, H., Wall, D., Heringdorf,\nF.M., et al. In situ observation of stress relaxation in epitaxial graphene. New\nJournal of Physics. 11, 113056 (2009)."}, {"round": 2, "reviewer_comments": {"reviewer_2": "It is a very good work in improving electrical conductivity of copper by defects. The author has given satisfactory responses to most of the comments, but I think there are still some issues require corrections and clarifications before its publishment in Nature Communications.\n1. The author supposed that the graphene at the grain boundaries will inhibit the grain coarsening during the heat treatment.\nHowever, the necessary premise is that graphene should be uniformly dispersed. According to the fabrication process of Gr-\nCu wires provided in Fig.R2, it is difficult to disperse graphene sufficiently by the volume fraction only ~0.004%.\n“Especially, only a small number of carbon atoms were detected using EELS in the deeply deformed Gr-Cu wire (Fig. R3h). ”\nwhat other factors could hinder grain coarsening apart from graphene.\n2. How to calculate the average grain size of Gr-Cu wires. Fig 2a shows lamellar structure of 50 μm wires, is the entire wire of this layered structure? Why Fig 1e shows different structure.\n3. Is the distorted nanolayer in Fig.2f regarded as a high velocity electronic pathway? Is it continuous or dispersed.\n4. Whether it is possible that the electrical conductivity was improved to ~110%IACS by introducing internal local stress\nusing other nano-particles.\n5. The author achieved extremely excellent electrical conductivity through structural design, but it is still puzzling that why\ndoes the method of increasing local stress lead to a better effect on improving electrical conductivity than that of eliminating\nstress?"}, "author_response": "Response to Reviewers’ Comments\nWe thank the Editor for the opportunity to revise our manuscript. We greatly appreciate\nthe reviewers for their valuable comments and professional advice.\nThese opinions are of very helpful for improving academic rigor of our article. Based\non your suggestions and requests, we have made corrections/modifications in the\nrevised manuscript. In the following sections, the reviewers’ comments are in red, and\nour responses to the comments are in black. Based on your suggestions and requests, we have made corrections/modifications in blue in the revised manuscript and\nSupplementary Information. We hope that our work can be improved again.\nFurthermore, we would like to show the details as follows.\nA List of Main Change Made\n1. TEM analyses of a new annealed Gr-Cu sample have been supplemented in Fig.\nRR4.\n2. The strain caused by graphene in different distributed states has been analyzed and\nquantified in R1.\n3. The volume fraction of graphene has been re-evaluated of ~0.004%-0.01% in\nSupplementary Note 1.\n4. Monte Carlo simulations have been supplemented in Fig. RR9 to reveal the\npinning effect of graphene on inhibiting grain coarsening.\n5. The calculation details of lattice strain (~5%) have been supplemented in\nSupplementary Note 3.\n6. The reasons for the maintenance of the lamellar structure's microstructure have\nbeen demonstrated in Fig. RR15.\n7. The calculation methods of the average grain size of Gr-Cu wires have been\nprovided.\n8. The compressive stress leading to high electrical conductivity has been analyzed\nand supplemented.\nResponses to Reviewers\nReviewer #2 (Remarks to the Author):\nRR1. The authors claim that the monolayer, bilayer, few-layer, and multilayer\ngraphene co-exist in their composites. Some follow-up questions are\nQ1: The stress level should be location dependent because of the various Gr thicknesses.\nAdditional localized stress analysis depending on Gr thickness would be beneficial. In\nother words, additional data will be needed to Figure 3 for accurate strain\nmeasurements.\nR1: Thanks for your suggestion. The interfacial stress was induced by the thermal\nexpansion coefficient (TEC) mismatch between the severely strained graphene and Cu\nmatrix. We systematically characterized and demonstrated the interlayer sliding of\nmultilayer graphene during the deformation process in our previous work1. As shown\nin Fig. RR1, single layer, few layer and multilayer graphene were dispersed on the grain\nboundaries (GBs) of Cu matrix. The interlayer sliding was also observed in this work\nusing in-situ TEM characterization (Supplementary Video 1). This is evidenced by the\ndifferent morphologies of graphene in the as sintered, as extruded and cold drawn Gr-\nCu samples (Fig. RR2).\nFig. RR1 | Molecular dynamics (MD) simulation showing interlayer sliding of graphene under\nshear stress1.\nIn this work, various graphene was observed in the cold drawn and annealed Gr-\nCu wires (Fig. RR2i-l). Typically, one-to-two layers and multilayer graphene were\ncharacterized in Fig. RR3. For monolayer graphene embedded in the Cu matrix, the\natomic-resolution image was difficult to be obtained2. Moreover, it was more\ncomplicated for the observation of graphene after severe drawing deformation ( ≈12).\nCarefully examination on the grain boundary of a random nanograin in the annealed\nGr-Cu wire using Electron energy loss spectroscopy (EELS) was conducted in Fig.\nRR3a, b. We observed an obvious carbon K edge. Under high-resolution TEM, we\nfound distorted nanolayers with a clear contrast exist along boundary. Quantitative\nanalysis indicates that the interplanar spacing of the Cu (111) was changed by ~10%.\nIn addition, multilayer graphene flakes could also cause lattice distortion. Figure RR3(h)\nshows a typical expansion of (200) interplanar spacing increased by ~27%, from ~1.80\nÅ to ~2.29 Å in the distorted nanolayer.\nFig. RR2 | SEM and TEM observations of Gr-Cu composites and graphene in different samples. a,\nc, f Gap-like grain boundaries (GBs) were widely distributed on the end face of the as-sintered and\nas-extruded Gr-Cu composites. b-d TEM characterization showing multilayer graphene distributed\non the boundary of the layered structure. g-h TEM characterization showing multilayer graphene\ndistributed on the boundary of the layered structure after extruding. i, j HRTEM images of the few-\nlayer graphene. k, l Graphene fragments were dispersed in the grain boundaries. i EELS spectra of the\ndispersed graphene in l.\nFig. RR3 | a, b TEM image and EELS spectrum of the ex-situ heating sample. c Distorted\nnanolayer observed in R1 region. d Magnification of the nanolayer in c. The blue and yellow box\nshowing the distorted lattice. e, f TEM image and EELS spectrum of the in-situ heating sample. g\nDistorted nanolayer observed in R3 region. h Typical severe lattice distortion due to the\ncompressed stress in the distorted nanolayers.\nIn addition to the changes of interplanar space, we also noticed that the strain could\ncause the lattice distortion (Fig. 3g). We further supplemented new TEM analyses of\nanother annealed Gr-Cu sample (Fig. RR4). Distorted Cu (111) lattice was observed in\nFig. RR4d. This distorted phenomenon was analogous with the results in Fig. 3g.\nRelevant revisions have been made on page 8.\nFig. RR4 | a-c TEM images and EELS spectrum of annealed Gr-Cu sample. d HAADF-STEM\nimages after heating showing typical severe lattice distortion due to the compressed stress.\nQ2: From the Raman map in Figure R4d, most regions show an I /I intensity of about\n2D G\n1 (green color), indicating that most of the Gr formed has a layer number around 2.\nOnly a very small portion of the map shows a multilayer signal. Therefore, the\ninterplanar distance change and the corresponding inference might not be\nrepresentative.\nR2: Thank you for your comments. The obtain of the Raman mapping involves a series\nof mathematical processing such as noise filter, subtract baseline, curve fit and batch\nprocessing, etc. Considering the testing time, the step size was 2 μm (Fig. RR5a and c).\nThus, the Raman mapping can only approximately characterize the distribution of\ngraphene. Further localized SEM-Raman characterization (Fig. RR5d and e) using a\nTESCAN RISE-MAGNA demonstrated that graphene with different layers was grown\non the Cu foil.\nFig. RR5 | Raman mapping measurement and SEM-Raman characterization. a The data\nprocessing procedure of Raman mapping. b Raman mapping. c Step size of 2 μm. d, e Optical\nmicroscope images and the corresponding Raman spot-scanning results.\nSubsequently, in order to precisely characterize the distribution of graphene, SEM\nand TEM characterization of the as-sintered Gr-Cu composite was carried out. As\nshown in Fig. RR6a-c, different Cu layers with thickness of ~25 μm were distinctly\nseparated by grain boundaries. The high-resolution HRTEM images demonstrated that\nmultilayer graphene was dispersed on a randomly selected grain boundary. Moreover,\nwe further conducted similar analysis on the as-extruded sample. Although the bulk Gr-\nCu composites underwent hot extrusion, gap-like morphologies (marked by white\nellipse) were widely distributed on the end face of the extruded bar. We also observed\nmultilayer graphene in the TEM sample from R2 region in Fig. RR6a. These\nobservations collectively suggest that most surface of the copper foil was grown\napproximately three to ten layers of graphene, rather than one to two layers indicated\nin the Raman mapping. Therefore, we roughly estimate the volume fraction of graphene\nis ~0.004%-0.01%, and the interplanar distance change as well as the corresponding\ninference are representative. Relevant revisions have been made on page 5 and\nSupplementary Note 1.\nFig. RR6 | SEM and TEM observations of Gr-Cu composites and graphene in different samples. a,\nc, f Gap-like grain boundaries (GBs) were widely distributed on the end face of the as-sintered and\nas-extruded Gr-Cu composites. b-d TEM characterization showing multilayer graphene distributed\non the boundary of the layered structure. g-h TEM characterization showing multilayer graphene\ndistributed on the boundary of the layered structure after extruding.\nRR2. (1): Laminar thickness decreasing from 25μm to ~175nm, resulting in an\ninterface area increasing by >100 times. If a three-layer Gr is assumed on average\n(although from the Raman map, most areas are covered by a 2-layer Gr), in the best\nscenario (all Gr have interlayer sliding and become monolayer Gr perfectly inserting\nthe interplane of Cu laminar), only a very limited fraction (<1%) of the interface\nbetween laminar Cu structures will is separated by Gr. However, in Figure 2D, 20%\nof the laminar structure remained after annealing, which may not be explained by the\nlimited amount of Gr.\nR1: Thank you for your comments. As mentioned in R2, considering the series of\nmathematical processing and the step size of 2 μm, the Raman mapping can only\napproximately characterize the distribution of graphene, the TEM characterization\nsampling from random GBs is more accurately to reflect the distribution of the in-situ\ngrown graphene on the Cu foil. As shown in Fig. RR6, the gap-like grain boundaries\n(GBs) were widely distributed on the end face of the as-sintered and as-extruded Gr-Cu\ncomposites. We also observed multilayer graphene sampling from the random gap-like\nGBs of the different Gr-Cu samples. These observations collectively suggest that most\nsurface of the copper foil was grown approximately three to ten layers of graphene,\nrather than one to two layers indicated in the Raman mapping.\nAs demonstrated in the MD simulation in Fig. RR1, the few layers and/or\nmultilayer graphene at GBs was thinned and further dispersed via shear induced\ninterlayer sliding during the subsequent hot extrusion and multi-pass cold drawing.\nFig. RR6 | Fig. RR6 | SEM and TEM observations of Gr-Cu composites and graphene in different\nsamples. a, c, f Gap-like grain boundaries (GBs) were widely distributed on the end face of the as-\nsintered and as-extruded Gr-Cu composites. b-d TEM characterization showing multilayer graphene distributed\non the boundary of the layered structure. g-h TEM characterization showing multilayer graphene\ndistributed on the boundary of the layered structure after extruding.\nTypically, as the drawing deformation continues, a portion of the graphene underwent\nfracture and dispersed on the GBs. We further conducted MD simulation to verify this\nhypothesis (Fig. RR7). Experimentally, as a consequence, various graphene distribution\nwas observed in the cold drawn and annealed Gr-Cu wires (Fig. RR8).\nFig. RR7 | MD simulation showing a portion of the graphene undergoing fracture and dispersed on\nthe GBs.\nAs the dispersed nanophase on the GBs, a large number of graphene flakes play\na role of pinning GBs and inhibiting grain coarsening. On the experimental side, we\nconfirmed this pinning effect based on microstructural analysis. As shown in Fig. 2d,\nthe nano-laminated structure was almost remained after annealing, and the grains\nslightly coarsened to an average grain size of 175 ± 138 nm.\nFig. RR8 | a, b HRTEM images of the few-layer graphene. c, d Graphene fragments were dispersed\nin the grain boundaries. e EELS spectra of the dispersed graphene in d.\nSimilar to most particle-reinforced phases, although the grain boundaries were\nnot fully covered with graphene, the effect of inhibiting coarsening was significant. We\nperformed Monte Carlo simulations using the open-source software SPPARKS3 to\nmodel grain growth during the simulated annealing of graphene-reinforced copper\nalloys at a constant temperature of 400 °C. As shown in the Fig. RR9, the dispersed\nphases at the grain boundaries effectively hinder grain growth by pinning the grain\nboundaries.\nFig. RR9 | Monte Carlo simulations showing the dispersed phases on the grain boundaries\ninhibiting grain coarsening due to the pinning effect.\n(2) Upon the heating process, compressive stress due to CTE is expected. However, the\nCTE-induced tensile stress is expected during the cooling process. How is the\ndetachment avoided in the cooling process after annealing, given that the MD\nsimulation shows the detachment will happen under tensile loading (Fig. R15).\nR2: Thank you for your suggestion. Due to the selected Lennard-Jones (LJ) potentials4,\ninterface detachment occurred only in the computational simulations, not in\nexperiments. With this potential, detachment of the Ni-C interface was also observed4.\nThese simulations hints that the LJ potential does not adequately capture the interfacial\nbonding strength. Then, we supplemented MD simulations using Morse potential5 to\nelucidate the maintaining effect of graphene on the mechanical properties of the\ngraphene-reinforced copper composites (Fig. RR10). The results demonstrate the\nremarkable increase in the tensile strength due to the hindering effect on the dislocations.\nFig. RR10 | Atomic configurations from MD simulation of Gr-Cu composite and Cu under tensile\nloading using Morse potential. a-c Gr-Cu composite. d, e Pure Cu. f Tensile stress-strain curves.\nFig. RR11 | Schematic of possible mechanism of fold6.\nIn this work, graphene tends to expand while Cu tends to shrink resulting in the\nformation of graphene wrinkles during the cooling process. and the compressive stress\nwas formed during the cooling6,7. Even though the interfacial compressive stress was\npartially released by forming folds or ripples, the majority of the compressive stress\nwas still retained. Under the compressive stress, such detachment phenomena are less\nlikely to occur5.\nRR3. See RR2 (1). In addition, please note the attached figure below. This review\nclearly indicates that surface scattering is not negligible. Do you have any comments\non this?\nFig. RR12 | a, Resistivity of Cu interconnects as a function of line width8. b, Variation of\nresistivity with thickness for Cu thin films9.\nR3: Thank you for your suggestion. Surface scattering is primarily caused by surface\nroughness and defects. Secondly, considering the quantum effect of the free electrons,\nFuchs and Sondheimer proposed a theoretical model (F-S model) to describe the\nvariation of electrical resistivity of metal thin films with thickness. We also noticed\nsome literatures on the electrical properties and the film thickness of Cu films8,9.\nHowever, as shown in Fig. RR12b, the electrical resistivity of Cu films is close to the\nbulk state value (1.67 μΩcm) at approximately 160 nm thickness9. Thus, the surface\nscattering and size-dependent resistivity are negligible in this work.\nRR5: Gr is in compressive stress while Cu is under tensile stress [11]. This is the\nopposite of the conclusion (extremely large compressive stress applied on Cu from Gr)\nin this study. Can you please clarify this?\nR5: Thank you for your question. During the heating process for the cold drawn Gr-Cu\ncomposite, the Cu matrix expanded whereas the graphene sheet contracted, thus\ninducing a tensile strain on graphene. However, contrary to the heating process,\ngraphene tends to expand while the Cu matrix tends to contract resulting in the\nformation of graphene wrinkles during the cooling process. As shown in Fig. RR11,\nthe interfacial compressive stress was partially released by forming folds or ripples,\nwhile the majority of the compressive stress was still retained. In this work, we just\nforced on the cooling process because the testing of electrical conductivity and the\nmicrostructure characterization were both conducted using the annealed Gr-Cu wires at\nroom temperature. Experimentally, the interfacial compressive stress was also revealed\nusing the high-resolution atomic configuration, synchrotron X-ray micro-diffraction (μ-XRD)\nand Raman measurements. Based on the above experimental results and theoretical\nanalysis, we concluded that the ultra-high electrical conductivity was induced by the\nlarge compressive stress.\nMinor\nRR1. The calculation of lattice strain (~5%) is crucial data, from which the improved\nelectrical conductivity is inferred. However, this strain level is estimated by Scherrer\nEquation and Bragg’ Law with the peak broadening of 1o-2o. No calculation details are\nprovided. Considering this 1 significant number of peak broadening, the incredibly low\nprecision significantly underlines the reliability of the conclusion of ~5% strain level.\nR1: Thank you for your suggestion. As shown in Fig. RR13a, in view of the Cu (111)\npeak position of ~15.5°, the interplanar spacing (d ) was determined of 2.08 Å\n111\naccording to the Bragg’s Law (2dsin, λ=0.563 Å, provided in Supplementary\nFig. RR13 | a As-integrated 1D synchrotron X-ray micro-diffraction patterns of the cold-drawn\nGr-Cu wire. b Anisotropic peak broadening and extra diffraction peaks in the 1D diffraction\npatterns of annealed Gr-Cu wire.\nTable 2). As a comparison, the approximate asymmetrical broadening range of 1.5° for\n2θ (from 15.5° to 17°) was observed in the μ-XRD diffraction pattern of the annealed\nGr-Cu sample. We estimated the average asymmetrical broadening value of ~0.75° (half\nof above broadening range), i.e., the Cu (111) gradually shifted to ~16.3° due to the\nlattice distortion. Thus, the strained interplanar spacing (d ) was determined of 1.98\n111\nÅ according to the Bragg’s Law. Consequently, the lattice strain was approximately\nestimated of ~5% using the equation of  =d /d . Relevant revisions have been made\n0\non Supplementary Note 3.\nRR4: If the local expansion and compression stress con-exist in the lattice, why only\nthe electrical conductivity of Cu matrix from compressive stress is considered?\nR4: Thank you for your question. In this work, the existence of compressive stress in\nthe annealed Gr-Cu wires was justified based on the TEM characterization, synchrotron\nX-ray micro-diffraction (μ-XRD) as well as the measurements of Raman spectra. The\nlocal expansion was observed in the TEM characterization, and we attributed this\nobservation to the interfacial compressive stress during annealing. Moreover, we also\napproximately estimated the compressive stress based on the asymmetrical broadening\nvalue of μ-XRD diffraction pattern and the Raman spectra. It should be noted that the\nasymmetrical broadening was on the right foot side of most of the diffraction peaks,\nthus indicating that the corresponding interplanar spacing was compressed.\nReviewer #3 (Remarks to the Author)\nIt is a very good work in improving electrical conductivity of copper by defects. The\nauthor has given satisfactory responses to most of the comments, but I think there are\nstill some issues require corrections and clarifications before its publishment in\nNature Communications.\nQ1: The author supposed that the graphene at the grain boundaries will inhibit the\ngrain coarsening during the heat treatment. However, the necessary premise is that\ngraphene should be uniformly dispersed. According to the fabrication process of Gr-\nCu wires provided in Fig.R2, it is difficult to disperse graphene sufficiently by the\nvolume fraction only ~0.004%.\n“Especially, only a small number of carbon atoms were detected using EELS in the\ndeeply deformed Gr-Cu wire (Fig. R3h). ”\nwhat other factors could hinder grain coarsening apart from graphene.\nR1: Thank you for your question. Considering the series of mathematical processing\nsuch as noise filter, subtract baseline, curve fit and batch processing, etc., and the step\nsize of 2 μm, the Raman mapping can only roughly characterize the distribution of\ngraphene, the TEM characterization sampling from random grain boundaries (GBs) is\nFig. RR6 | SEM and TEM observations of Gr-Cu composites and graphene in different samples. a,\nc, f Gap-like grain boundaries (GBs) were widely distributed on the end face of the as-sintered and\nas-extruded Gr-Cu composites. b-d TEM characterization showing multilayer graphene distributed\non the boundary of the layered structure. g-h TEM characterization showing multilayer graphene\ndistributed on the boundary of the layered structure after extruding.\nmore accurately to evaluate the distribution of the in-situ grown graphene on the Cu\nfoil. As shown in Fig. RR6, the gap-like GBs were widely distributed on the end face\nof the as-sintered and as-extruded Gr-Cu composites. We also observed multilayer\ngraphene sampling from the random gap-like GBs of the different Gr-Cu samples. For\ninstance, although the bulk Gr-Cu composites underwent hot extrusion, gap-like\nmorphologies (marked by white ellipse) were widely distributed on the end face of the\nextruded bar. These observations collectively suggest that most surface of the copper\nfoil was grown approximately three to ten layers of graphene, rather than one to two\nlayers indicated in the Raman mapping. Therefore, we approximately estimated the\nvolume fraction of graphene of ~0.004%-0.01% instead of the 0.004% in the\nSupplementary Note 1.\nWe systematically characterized and analyzed the interlayer sliding of multilayer\ngraphene during the shearing process in our previous work1. As shown in Fig. RR14a,\nsingle layer, few layer and multilayer graphene were dispersed in grain boundaries of\nCu matrix. The interlayer sliding was also observed in this work using in-situ TEM\nanalysis (Supplementary Video 1). Experimentally, laminated structure assembling and\nregulating the drawing direction as well as the interlayer sliding could ensure that the\ngraphene was fully dispersed. However, as the severe drawing deformation continued,\na portion of the graphene would undergo fracture and dispersed on the grain boundaries.\nFig. RR14 | a Molecular dynamics (MD) simulation showing interlayer sliding of graphene under\nshear stress1. b-d MD simulation showing a portion of the graphene undergoing fracture and\ndispersed on the grain boundaries.\nSimilar to most particle-reinforced phases, although the grain boundaries were not\nfully covered with graphene, the effect of inhibiting coarsening was significant. We\nperformed Monte Carlo simulations using the open-source software SPPARKS3 to\nmodel grain growth during the simulated annealing of graphene-reinforced copper\nalloys at a constant temperature of 400 °C. As shown in the Fig. RR9, the dispersed\nphases at the grain boundaries effectively hinder grain growth by pinning the grain\nboundaries.\nFig. RR9 | Monte Carlo simulations showing the dispersed phases on the grain boundaries\ninhibiting grain coarsening due to the pinning effect.\nIn addition to graphene, low-energy grain boundaries play a significant role in\nsuppressing coarsening. For instance, statistical results showed that the fraction of twin\nboundaries (TBs) in the cold drawn Gr-Cu sample was 11% (Supplementary Fig. 12).\nSecondly, strong <111> and/or <100> fiber texture was detected indicating the\nformation of a large number of low-angle grain boundaries, thus improving the thermal\nstability (Supplementary Fig. 11 and Supplementary Fig. 12).\nQ2: How to calculate the average grain size of Gr-Cu wires. Fig 2a shows lamellar\nstructure of 50 μm wires, is the entire wire of this layered structure? Why Fig 1e shows\ndifferent structure.\nR2: Thank you for your question. Firstly, all the calculations of the average grain size\nof Gr-Cu wires were made by the linear-intercept method. Secondly, laminated\nstructure assembling and regulating the drawing direction as well as the interlayer\nsliding could ensure the evolution of the layered structure. As shown in Fig. RR15, as\nthe drawing process continued, nanograined structures were formed and retained in the\nfinal deep cold drawn Gr-Cu wires. Thus, the entire wire was filled with this layered\nstructure. This layered structure was also revealed by the drawing direction-normal\ndirection (DD-ND) cross-sectional inverse pole figure (IPF) map of cold drawn wire\n(Fig. RR15e).\nDifferent from the layered structures of the cold drawn Gr-Cu wires, Fig. 1e is the\nmicrostructure of the annealed Gr-Cu wires. Thus, some grains underwent coarsening\nduring the annealing process, whereas the other grains retained layered structure due\nthe inhibiting coarsening by graphene.\nFig. RR15 | a Schematic illustration of the fabrication process of Gr-Cu wires. b, c SEM images\nof the cross-sectional microstructure of as sintered and as extruded Gr-Cu samples. d Band\ncontrast map of the cross-sectional microstructure of Gr-Cu wire characterized using precession\nelectron diffraction (PED). e DD-ND cross-sectional IPF maps of cold drawn samples with\ndiameter of 0.05 mm.\nQ3: Is the distorted nanolayer in Fig.2f regarded as a high velocity electronic pathway?\nIs it continuous or dispersed.\nR3: Thank you for your question. Under high-resolution TEM, we found distorted\nnanolayers with a clear contrast exist along boundary (Fig. 2f). According to relevant\nliterature reports10-12, the graphene plays an important role in providing high velocity\npathways for phonons and electrons. It should be noted that these findings were based\non the premise that the structure of graphene was relatively intact. Besides, the layers\nnumber of graphene has a significant impact on the electrical conductivity. However,\nthe graphene in this work was thinned and further dispersed via shear induced interlayer\nsliding during the cold drawing (Fig. RR15a and Supplementary Video 1). And it has\nbecome almost impossible for graphene to maintain its inherent intact structure.\nConsequently, we attributed the high conductivity to the giant interfacial stress exerted\non the Cu matrix, thus suppressing electron-phonon coupling. In a sense, the influence\nregions (distorted nanolayer) of the interfacial stress in the Cu matrix may also be\nregarded as a “high velocity pathways”. And it is dispersed in the Cu matrix due to the\nlarge cold drawing deformation.\nQ4: Whether it is possible that the electrical conductivity was improved to ~110%IACS\nby introducing internal local stress using other nano-particles.\nR4: Thank you for your question. Our work indicates that abundant GBs with distorted\nlattice due to giant compressive stress induced by the thermal expansion coefficient\n(TEC) mismatch in the nanograined Cu enable an exceptional electrical conductivity.\nIt provides an effective approach to enhance electrical conductivity and mechanical\nstrength simultaneously. It is possible to achieve high electrical conductivity by\napplying to many other two-dimensional (2D) materials /copper systems on the premise\nthat these 2D materials have a negative coefficient of thermal expansion.\nQ5: The author achieved extremely excellent electrical conductivity through structural\ndesign, but it is still puzzling that why does the method of increasing local stress lead\nto a better effect on improving electrical conductivity than that of eliminating stress?\nR5: Thank you for your question. Traditionally, eliminating stress can reduce electrons\nscattering resulting in improving the electrical conductivity. This stress usually\noriginates from the cold deformation process. Hence, annealing is usually employed to\neliminating stress to restore the electrical conductivity of conducting metals. However,\nthe effect based on the annealing is very limited. In this work, giant interfacial\ncompressive stress was induced due to the different TEC during annealing, thus\nsignificantly suppressing electron-phonon coupling and reducing phonon-caused\nelectron scattering. This giant interfacial compressive stress has been demonstrated\nbased on the TEM characterization and synchrotron X-ray micro-diffraction (μ-XRD)\nas well as the measurements of Raman spectra. And this compressive stress is\ncompletely different from the stress caused by the cold deformation. Moreover, with\nintroduction of the interfacial compressive stress, defects such as dislocations and\nvacancy have also been eliminated through annealing.\nReferences\n1. Zhang, X., Xiong, D. B., Liu, Y., Jia, Y., Zhang, Y., Zhou, M., Liu, H., Geng, Y.,\nWang, X., Liu, P., Song, X., Zhang, D. Multilayer graphene interface enabled\nultrahigh extensibility for high performance bulk nanostructured copper. Acta\nMater. 267, 119710 (2024).\n2. Jinschek, J.R., Yucelen, E., Calderon, H.A., Freitag, B. Quantitative atomic 3-D\nimaging of single/double sheet graphene structure. Carbon. 49, 556-562 (2011).\n3. Mitchell, J. A., Abdeljawad, F., Battaile, C., et al. Parallel simulation via\nSPPARKS of on-lattice kinetic and Metropolis Monte Carlo models for materials\nprocessing. Modelling and simulation in materials science and engineering.\n31(5), 055001 (2023).\n4. Duan, K., Zhu, F., Tang, K., He, L., Chen, Y., Liu, S. Effects of chirality and\nnumber of graphene layers on the mechanical properties of graphene-embedded\ncopper nanocomposites. Comput. Mater. Sci. 117, 294-299 (2016).\n5. Makan, M., Makan, A., Ghoulbzouri, A.E. Effect of graphene network\nreinforcement and interface orientation on the mechanical behavior of nickel\ncomposites: A molecular dynamics study. Acta Mater. 284, 120637 (2025).\n6. Wang, M., Huang, M., Luo, D., Li, Y., Choe, M., Seong, W.K., et al. Single-crystal,\nlarge-area, fold-free monolayer graphene. Nature. 596, 519-524 (2021).\n7. Hattab, H., N’Diaye, A.T., Wall, D., Klein, C., Jnawali, G., Coraux, J., et al.\nInterplay of wrinkles, strain, and lattice parameter in graphene on Iridium. Nano\nLetters. 12, 678-682 (2012).\n8. N’Diaye, A.T., Gastel, R., Martínez-Galera, A.J., Hattab, H., Wall, D., Heringdorf,\nF.M., et al. In situ observation of stress relaxation in epitaxial graphene. New\nJournal of Physics. 11, 113056 (2009).\n9. Josell, D., Brongersma, S.H., To˝kei, Z. Size-Dependent Resistivity in Nanoscale\nInterconnects. Annual review of materials research. 39, 231-254 (2009).\n10. Khojier, K., Savaloni, H. A study on the dependence of DC electrical properties\nand nanostructure of Cu thin films on film thickness. Int. J. Nano Dimens. 3, 217-\n226 (2013).\n11. Morozov, S.V., Novoselov, K.S., Katsnelson, M.I., et al. Giant intrinsic carrier\nmobilities in graphene and its bilayer. Physical Review Letters. 100:016602 (2008).\n12. Bolotin, K.I., Sikes, K.J., Jiang, Z., Klima, M., Fudenberg, G., Hone, J., Kim, P.,\nStormer, H.L. Ultrahigh electron mobility in suspended graphene. Solid State\nCommunications. 146: 351-355 (2008).\n13. Cao, M., Xiong, D. B., Yang, L., Li, S. S., Xie, Y., Guo, Q., Li, Z., Adams, H., Gu,\nJ., Fan, T., Zhang, X., Zhang, D. Ultrahigh electrical conductivity of graphene\nembedded in metals. Adv. Funct. Mater. 29, 1806792 (2019)."}, {"round": 3, "reviewer_comments": {"reviewer_2": "The authors have addressed my previous comments, and I recommend the publication of the manuscript without further changes.", "reviewer_3": "1)I think the author deliberately confused cold drawing with deep cold drawing. The process used here should be conventional cold drawing on line 418 rather than deep cold drawing on line 79, 119 and 181\n2)Line 325, “30 GPa pressure was needed based on density functional theory (DFT) calculations, which is rational and expected in the deep cold drawn wire ….” Here the deep cold drawing (maybe ultra high pressure or other non extreme condition) is different from the processing in this study, cold drawing and heat treatment processes cannot achieve this effect of electron-phonon coupling, therefore, this theory is insufficient to support the discussion here.\n3)The formation of defects of severely distorted lattice is induced by the heterogeneous interface between graphene and copper, does this mean that the arrangement of these defects is directional (along the drawing direction)? Then, in the discontinuous regions of graphene, is there any difference in the arrangement of such defects?"}, "author_response": "Response to Reviewers’ Comments\nWe thank the Editor for the opportunity to revise our manuscript. We greatly appreciate\nthe reviewers for their valuable comments and professional advice during the previous\nrounds of review process. These opinions are of very helpful for improving academic\nrigor of our article. Based on your suggestions and requests, we have made\ncorrections/modifications in the revised manuscript. In the following sections, the\nreviewers’ comments are in red, and our responses to the comments are in black. Based\non your suggestions and requests, we have made corrections/modifications in blue in\nthe revised manuscript and Supplementary Information. We hope that our work can be\nimproved again. Furthermore, we would like to show the details as follows.\nA List of Main Change Made\n1. The confused expressions on the drawing process have been revised on line 79,\n119 and 181.\n2. The discussion of the pressure in the experimental and DFT simulation effect on\nthe suppression of electron-phonon coupling has been supplemented and revised.\n3. The compressive stress induced on the graphene-wrapped nanograin has been\nsupplemented in Supplementary Fig. 21.\nResponses to Reviewers\nReviewer #2 (Remarks to the Author):\nQ1: The authors have addressed my previous comments, and I recommend the\npublication of the manuscript without further changes.\nR1: We sincerely thank you for the valuable comments and guidance during the\nprevious rounds of review process.\nReviewer #3 (Remarks to the Author):\nQ1: I think the author deliberately confused cold drawing with deep cold drawing. The\nprocess used here should be conventional cold drawing on line 418 rather than deep\ncold drawing on line 79, 119 and 181.\nR1: Thanks for your comments. We apologize for this inadvertent confused cold\ndrawing with deep cold drawing. Based on literature reports1,2, deep drawing is a metal\nforming process for fabricating seamless, sheet metal parts, which are closed on one\nend with a depth greater than radius. We intended to express that the Gr-Cu wire\nunderwent dramatic deformation during the cold drawing process, i.e. the extruded bar\n(diameter d = 13 mm) can be continuously cold drawn to wires (d < 0.03 mm) without\nintermediate thermal annealing (corresponding to a strain of ~12, Supplementary Fig.\n2 and Supplementary Fig. 3). The relevant confused wording has been revised on line\n79, 119 and 181.\nQ2: Line 325, “30 GPa pressure was needed based on density functional theory (DFT)\ncalculations, which is rational and expected in the deep cold drawn wire ….” Here the\ndeep cold drawing (maybe ultra high pressure or other non extreme condition) is\ndifferent from the processing in this study, cold drawing and heat treatment processes\ncannot achieve this effect of electron-phonon coupling, therefore, this theory is\ninsufficient to support the discussion here.\nR2: Thank you for your comments. In present work, the few-layer graphene at grain\nboundaries (GBs) was thinned and further dispersed via shear induced interlayer sliding\n(Supplementary Fig. 10 and Supplementary Video 1), and plays the role of inhibiting\ndynamic recovery and recrystallization against plastic deformation. As results, the\nlamellae were continuously thinned and finally refined to nanoscale (Supplementary\nFig. 11 and Fig. RRR1b). Giant interfacial stress induced by the thermal expansion\ncoefficient (TEC) mismatch between the severely strained graphene and Cu matrix (Fig.\nRRR1c). Experimentally, the interfacial compressive stress was also revealed using the\nhigh-resolution atomic configuration, synchrotron X-ray micro-diffraction (μ-XRD)\nand Raman measurements.\nIn term of the 30 GPa pressure, the hydrostatic pressure is simulated by change\nthe crystal parameters in the density functional theory (DFT) calculations. From a\nstress-origin perspective, there is a little difference between the aforementioned\ninterfacial compressive stress and the hydrostatic pressure in DFT calculations.\nHowever, similar compressive strain increasing the conductivity was also confirmed\nusing experimental test and simulated calculation in the copper/graphene composites3.\nBesides, it was recently proposed that the electrical resistivity decreases in aluminum\nand copper wires upon pressuring each metal4 (Fig. RRR1d). If the graphene-wrapped\nnanograin in the Fig. RRR1c is analogized to a copper wire, its compressive stress state\nis similar to that reported in the literature4. Notably, similar experimental and simulation\nresults on compressive stress suppressing electron-phonon coupling to enhance the\nconductivity of Au have also been reported in our recent work5. And we have revised\nthe relevant discussion to more sufficiently explain the suppression of electron-phonon\ncoupling by interfacial compressive stress.\nFig. RRR1 | Compressive stress induced on the graphene-wrapped nanograin. a, b Schematic\nillustration and TEM image showing the nanograin in the cylindrical cross-section of Gr-Cu wire.\nc Schematic illustration of the cylindrical cross-section of annealed Gr-Cu wire showing the\ncompressive stress induced on the graphene-wrapped nanograin due to TEC mismatch. d\nSchematic drawing of a solid media pressure-cell in the literature4.\nQ3: The formation of defects of severely distorted lattice is induced by the\nheterogeneous interface between graphene and copper, does this mean that the\narrangement of these defects is directional (along the drawing direction)? Then, in the\ndiscontinuous regions of graphene, is there any difference in the arrangement of such\ndefects?\nR3: Thank you for your question. Experimentally, laminated structure assembling and\nregulating the drawing direction as well as the interlayer sliding could ensure that the\ngraphene was fully dispersed along the drawing direction (Supplementary Fig. 9,\nSupplementary Fig. 10). Thus, the arrangement of these defects (distorted lattice) is\ngenerally along the drawing direction. As the reviewer pointed out, a portion of the\ngraphene underwent fracture (discontinuous regions of graphene) and dispersed on the\nGBs as the drawing deformation continues. These graphene-discontinuous regions\nunderwent localized grain coarsening during the annealing process. We also\nsystematically characterized these regions and observed no obvious strained nanolayers\nand/or the distorted lattice analogous to those observed in Fig. 2f and Fig. 3a-d.\nReferences\n1. Zhao, H., Ma, X, Wang, Z., Jiang, Z., Zhou, C., Zhao, J. Surface roughness\nevolution and heterogeneous plastic deformation of austenitic stainless steel\nduring micro deep drawing: Modeling and experiment. Int. J. Plast. Mater. 176,\n103964 (2024).\n2. Yi, S., Bohlen, J., Heinemann, F., Letzig, D. Mechanical anisotropy and deep\ndrawing behaviour of AZ31 and ZE10 magnesium alloy sheets. Acta Mater. 58,\n592-605 (2010).\n3. Zhang, C., Xiao, Z., Paddock, R., Cullinan, M., Tehrani, M., Liu, Y. Effects of\ngraphene doping on the electrical conductivity of copper. Adv. Funct. Mater. 34,\n2407569 (2024).\n4. Lanzillo, N. A., Thomas, J. B., Watson, B., Washington, M., Nayak, S. K.\nPressure-enabled phonon engineering in metals. Proc. Natl. Acad, Sci. 111, 8712-\n8716 (2014).\n5. He, S., Zhang, X., Xiong, D.B. Thickness effect on strain coefficient of electrical\nresistance in metal nanofilms and regulation by composite with graphene. Appl.\nSurf. Sci. 716, 164703 (2026)."}, {"round": 4, "reviewer_comments": {"reviewer_3": "I have no questions about the submitted manuscript."}, "author_response": ""}]

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