Nanotwin architecture and ultra-high valley degeneracy lead to high thermoelectric performance in GeTe-based thermoelectric materials

Domain: physics
Published: 2026-01-31
Editorial outcome: major_revision

Abstract
Here, we achieve a high peak ZT of 2.5 as well as an exceptional average ZT of 1.9 through nanotwin architecture and inducing ultra-high valley degeneracy. We find that nanotwins, ordered vacancy arrays and point defects serve as intense phonon scattering centers for enhancing wide-frequency phonon scattering, resulting in ultra low lattice thermal conductivity in GeTe. Interestingly, density-functional theory calculations reveal that CuBiS2 alloying realizes refined valence band alignment in GeTe, generating an ultra-high valley degeneracy of 22. The dramatic enhancement of the Seebeck coefficient induced by the ultra-high valley degeneracy contributes to remarkably enhanced power factor over a very wide temperature range. The maximum power factor reaches as high as 49 μW cm-1 K-2. Consequently, a high peak ZT as well as a large average ZT are realized in GeTe without involving toxic elements. Importantly, the presence of nanotwins boundaries in GeTe effectively provides adequate barriers to block dislocation motion, leading to excellent hardness and compressive strength. Our finding provides a feasible pathway to design fascinating thermoelectric materials with high thermoelectric performance and mechanical properties.

Introduction
Thermoelectric materials and devices can realize direct inter- conversion between electricity and waste heat based on charge carrier and phonon transport only, showing great potential in power generation and electronic cooling1. The energy conversion efficiency is primarily related to the dimensionless figure of merit (ZT=S2σT/κT), where σ, S, κT, and T denote the electrical conductivity, Seebeck coefficient, total thermal conductivity and absolute temperature, respectively2,3. κT comprises both electronic thermal conductivity κe and lattice thermal conductivity κL, expressed as κT =κe +κL. S2σ can be expressed in terms of power factor (PF=S2σ), which is commonly used to represent the electrical transport properties of the material. However, strong interdependence among thermoelectric parameters prevents us from maximizing the final ZT and energy conversion efficiency4,5.

PbTe, with a leading thermoelectric performance, has been used for power generation applications and space exploration missions6,7. Yet, the environmentally hazardous element Pb is creating pollution problems. GeTe has attracted extensive research owing to both its high thermoelectric performance and environmentally friendly features. GeTe undergoes a ferroelectric phase transition from the low-temperature rhombohedral phase (r-GeTe) to the high-temperature cubic phase (c-GeTe) at approximately 670 K, driven by the lone pair effect of Ge atoms, which induces Peierls distortion through their displacement along the [111] direction in two sublattices8–10. The improved lattice symmetry during phase transition will increase the valley-degeneracy (Nv) and provide an additional degree of freedom for optimizing the thermoelectric properties11. High intrinsic carrier concentration (~1021 cm-3) induced by the low forming energy of Ge vacancy results in much inferior thermoelectric performance in pristine GeTe10,12. Carrier concentration modulation via heterovalent doping by Bi13 and Sb14 doping has been demonstrated as an effective strategy to enhance the thermoelectric properties of GeTe, and increase formation energy of Ge vacancies can also decrease carrier concentration15,16. Band convergence, achieved through Cd17, Zn18, Ca19, and Hg20 doping in GeTe by reducing the energy offset between heavy and light bands, alongside resonance levels introduced by In21 and Ga22 doping that create a hump near the Fermi level in the density of states, both effectively enhance the Seebeck coefficient. Enhancing phonon scattering through lattice imperfections (e.g., point defects23, vacancy clusters24, dislocations25, and planar vacancies26), secondary phases27, and grain boundaries28 serve as the primary strategy for reducing lattice thermal conductivity.

However, many of the above-mentioned strategies primarily focus on enhancing peak ZT, which constrains the energy conversion efficiency and practical application. Thermoelectric properties of GeTe systems have not yet reached the theoretical optimum10,29. Developing highly effective GeTe with not only high peak ZT but also high average ZT over a wide temperature range is a priority for achieving high conversion efficiency. Additionally, GeTe-based thermoelectric materials exhibit limited mechanical properties. It is a great challenge to simultaneously achieve highly competitive thermoelectric performance and good mechanical properties in thermoelectrics. Twin boundaries can act as intense phonon scattering center, improving thermoelectric properties by suppressing the lattice thermal conductivity30. In the meantime, twin boundaries also can lead to strengthening effect and enhanced mechanical performance31. Electronically, the construction of nanostructures inevitably induces carrier scattering, thereby degrading electrical properties. To overcome this drawback, band convergence of electron valence band edges can remarkably increase Nv to provide additional carrier transport channels for optimizing electrical transport performance.

Here, a strategy of synergy of nanotwin architecture and inducing ultra-high valley degeneracy was proposed for simultaneously achieving high thermoelectric performance as well as excellent mechanical properties in GeTe (Fig. 1). Dense nanotwins combined with vacancy arrays and point defects significantly diminish lattice thermal conductivity by strengthening wide-frequency phonon scattering (Fig. 1a). In the meanwhile, an ultra-high Nv of 22 was induced via refined valence band alignment between the three valence band maxima by CuBiS2 alloying (Fig. 1b), resulting in largely enhanced power factor over the whole temperature range. Resultantly, these synergistic effects contributed to a peak ZT value of 2.5 and an average ZT of 1.9 across the temperature range of 400-823 K in GeTe (Fig. 1c). Furthermore, nanotwins boundaries contribute to excellent mechanical properties in GeTe by hindering dislocation motion and accommodating dislocations. This work establishes a paradigm for high-efficiency and reliable thermoelectric materials design.

Results
Crystal structure and phase description
Powder X-ray diffraction (XRD) patterns of (GeTe)1-x(CuBiS2)x samples shown in Fig. 2a well match the rhombohedral GeTe structure (space group R3m)32. Extra peaks of Ge precipitates can be detected, which is an unavoidable phenomenon in GeTe system due to the low formation energy of Ge vacancies32,33. As the CuBiS2 alloying content reaches x=0.09, distinct diffraction peaks indexed to the secondary phase of CuBiS2 were observed. This suggests that the solubility limit of CuBiS2 in GeTe is lower than 9%. On the other hand, the position of (024) and (220) peaks shift toward lower angles and gradually merge with the increase of CuBiS2 (Fig. 2b), implying the expansion of lattice and increase of lattice symmetry34. Rietveld refined XRD patterns and the refinement details can be found in Fig. 2c, d and Supplementary Fig. 1, respectively. Figure 2d clearly show that the lattice constant a and b increase from 4.16 Å to 4.20 Å with increasing CuBiS2 alloying content, which can be attributed to the fact that the ionic radii of Bi3+ (1.03 Å) and Cu+ (0.77 Å) are both larger than that of Ge2+ (0.73 Å). The occupied positions of the corrected atoms are exhibited in Supplementary Table 1. It is found that the Cu and Bi atoms occupy the Ge site (Wyckoff position 2c) with coordinates of (0, 0, 0.2437), while the S atoms occupy the Te site (Wyckoff position 2c) with coordinates of (0, 0, 0.7629). Furthermore, the phase constitution and quantitative phase fractions present in the alloyed samples are clarified (Supplementary Table 2). It proves the good dissolution of CuBiS2 in GeTe when the alloying content is less than or equal to x=0.07. Because the phase transition progress from r-GeTe to c-GeTe is caused by center cation atom shifting along the [111] direction (Peierls distortion), we can use the lattice angle α to represent the lattice symmetry10. The lattice angle α enlarges from 58° to 58.8°, confirming the enhanced lattice symmetry induced by CuBiS2 alloying. The differential scanning calorimetry (DSC) investigations in Fig. 2e were performed to investigate the phase transition temperature of (GeTe)1-x(CuBiS2)x samples. The phase transition temperature (Tp) decreases with the increase of CuBiS2 content (Fig. 2f). In particular, the phase transition temperature gradually shifted down to ~586 K with x=0.07, which is about 70 K lower than the pure GeTe. The reduced phase transition temperature further indicates that the lattice symmetry of GeTe has increased, which extends the superior thermoelectric transport behavior of cubic phase to low temperatures21,35. The fracture morphology suggests the sample is very compact with no pores (Supplementary Fig. 2). The relative density of all the samples exceeds 96% (Supplementary Table 3), confirming the highly compact nature of the sample.

Thermal transport properties
The temperature-dependent total thermal conductivity (κT) experienced a sharp decrease after CuBiS2 alloying across the whole temperature range compared to the pure GeTe (Fig. 3a). To determine the factors responsible for the variation in κT, the temperature-dependent electrical thermal conductivity (κe) is calculated according to the equation of Wiedemann-Franz law (κe = LσT). The Lorenz number (L) is calculated by fitting respective Seebeck coefficient values with an assumption of a single parabolic band (SPB) model (Supporting Information), as illustrated in Supplementary Fig. 3. κe was greatly suppressed because of the reduced σ, which is partially responsible for the reduced κT. The rising trend of κe at high temperature is caused by electron thermal excitation. By subtracting κe from the κT, we achieved the lattice thermal conductivity (κL) in Fig. 3b. It is demonstrated that the κL of all the CuBiS2 alloying samples is effectively suppressed in the whole temperature range and decreases with the rising alloying content. However, an anomalous increase overshadows the decreasing trend at high temperatures, indicating bipolar thermal-conduction activation. The lowest κL of best performance (GeTe)0.93(CuBiS2)0.07 sample is restrained to ~0.38 W m-1 K-1 at 673 K, a value close to the Cahill model theoretical limit (~0.3 W m-1 K-1) of GeTe36, which is lower than most recent reported GeTe systems (Supplementary Fig. 4)37–43.

Microstructural characterization
To elucidate the underlying mechanism of markedly reduced κL, microstructural characterization was carried out utilizing scanning transmission electron microscopy (STEM). In the high-angle annular dark-field (STEM HAADF) images of Supplementary Fig. 5, the strip ferroelectric domains are found in the matrix. In the meantime, abundant nanotwins can be found in the matrix, as shown in Fig. 4a. The magnified image (Fig. 4b) clearly show the domain wall between the twin structures. The atomic-level (high-resolution transmission electron microscopy, HRTEM) image of nanotwins is shown in Fig. 4c. It is clear that the atomic arrangements exhibit mirror symmetry across the twin boundaries, which is the typical structure of nanotwins. FFT (fast Fourier transformation) pattern of Fig. 4c for nanotwins, spot splitting away from the transmitted beam (T) was observed (Fig. 4d). This further confirms the twin structures. The intensity in the STEM HAADF image is approximately proportional to the atomic number Z2. Z-contrast intensity profiles of Te and Ge atomic columns taken from Fig. 4c with corresponding histograms are presented in Fig. 4e, i and f, and j. The reddish hues correspond to heavier elements, while bluish tones indicate lighter elements and vacancies. The intensity distribution of Te columns is more uniform than that of Ge columns, the Z-contrast intensity of the Ge atomic columns exhibits significant local variations (inhomogeneity), indicating pronounced compositional fluctuations at the microscopic scale. Such local compositional fluctuations serve as a key microstructural mechanism for introducing mass-field perturbations and enhancing phonon scattering. Additionally, due to the low formation energy of Ge vacancies, such vacancies likely present in the matrix also appear as blue signals.

The random substitution of atoms with varying masses within the GeTe lattice introduces local mass fluctuations, which enhance phonon scattering and significantly reduce thermal conductivity. Bond length calculations for both Te and Ge sites are shown in Fig. 4g, k and h, l. Reddish lines denote longer bonds, bluish lines represent shorter bonds, and green lines indicate the average bond lengths. The Te–Te and Ge–Ge bond lengths fluctuate in the range of 94–107% and 94–109% of their average values, respectively. This bond-length variation is attributed to local lattice strain induced by nanotwins, which results in a more flexible lattice framework. The softened lattice promotes large-amplitude atomic vibrations, significantly enhancing anharmonic effects and thereby strengthening phonon scattering, which leads to a notable reduction in thermal conductivity.

Ordered vacancy arrays can be observed in the HRTEM image in Fig. 5a, and the corresponding (geometric phase analysis) GPA map is exhibited in Fig. 5b–d. GPA analysis indicates a large average lattice strain fluctuation, suggesting the presence of localized lattice strain at the vacancy arrays. Atomic-resolution HAADF image of the ordered vacant arrays is illustrated in Fig. 5e. Along this zone axis, Ge and Te atomic columns exhibit distinct contrast: Ge columns appear smaller and dimmer due to lower atomic number, while Te columns display larger, brighter features. The corresponding intensity line profile along the yellow frame from the atom arrays in Fig. 5f also confirms the ordered vacant arrays. The schematic of the atom array of vacancy arrays and the complete lattice was shown in Fig. 5g to better understand the difference between them. Z-contrast intensity profiles and bond length calculations for Te and Ge atomic columns are presented in Fig. 5h–k. Flanking the ordered Ge-vacancy chains, a decrease in Te-column intensity alongside an increase in Ge-column intensity indicates the substitution of Te sites by lighter atoms and Ge sites by heavier atoms, facilitating the formation of one-dimensional ordered Ge-vacancy chains. The ordered vacancy arrays introduce localized mass fluctuations and lattice strain, leading to lattice softening and a reduction in the lattice thermal conductivity.

Overall, the enhanced point defects lead to strong phonon scattering, thereby reducing the lattice thermal conductivity. Abundant nanotwins significantly enhance anharmonic effects and thereby strengthening phonon scattering through lattice softening, leading to a notable reduction in thermal conductivity. Furthermore, the ordered vacancy arrays significantly suppress the lattice thermal conductivity by introducing localized mass fluctuations and lattice strain. As a result, a remarkably low lattice thermal conductivity (0.38 W m-1 K-1) is achieved in (GeTe)0.93(CuBiS2)0.07, benefiting from a constructed defect complex including point defects, nanotwins, and ordered vacancy arrays in GeTe.

To visualize the effects of various scattering center on the decreased κL, the frequency dependent spectral lattice thermal conductivity (κs) for (GeTe)0.93(CuBiS2)0.07 sample is simulated by Debye-Callaway model (Supporting Information)44, as shown in Fig. 3c, considering the contribution of Umklapp scattering process (U), normal scattering process (N), point defect scattering process (PD), grain boundaries and twin boundaries scattering process (B), vacant arrays scattering process (VA) (the detail parameters are listed in Supplementary Table 4). It is clearly shown that the point defects can largely scatter the medium and high-frequency phonons. Twin boundaries and vacancy arrays are another important mechanism to scatter low and medium-frequency phonons. The theoretical κL is calculated and compared with the experimental value in Fig. 3d. The calculated results confirm that nanotwins, ordered vacancy arrays, and point defects indeed significantly reduce the lattice thermal conductivity of GeTe. The defect complex, including nanotwins, ordered vacancy arrays, and point defects, serves as intense phonon scattering centers for enhancing wide-frequency phonon scattering (Fig. 1a), thus contributing to the greatly suppressed κL for the (GeTe)0.93(CuBiS2)0.07 sample.

Electrical transport properties
The temperature-dependent electrical conductivity (σ) of (GeTe)1-x(CuBiS2)x samples is shown in Fig. 6a. σ decreases with increasing CuBiS2 alloying content. (GeTe)0.93(CuBiS2)0.07 material exhibits lowest σ in the whole temperature range. The sudden change of σ from 550 to 670 K can be attributed to the valance band switch between L and Σ points induced by phase transition27. Hall measurements were performed to determine the carrier concentration (n) and carrier mobility (μ), as illustrated in Fig. 6c. The carrier concentration decreases with the increasing content of CuBiS2. The n decreases from 6.5 × 1020 cm-3 for pure GeTe to 2.28 × 1020 cm-3 for (GeTe)0.93(CuBiS2)0.07 sample, which is suppressed to the optimal region for GeTe system. Bi serves as a donor dopant, effectively providing a large number of extra electrons, which can compensate for the intrinsic high hole concentration in GeTe45. In the meanwhile, the introduction of Cu is an efficient dopant for decreasing hole concentration by increasing the vacancy formation energy46. μ experienced a sharp decrease after CuBiS2 alloying due to enhanced point defect scattering. The reduced carrier concentration and carrier mobility lead to the decline in σ.

The temperature dependence of the Seebeck coefficient (S) for (GeTe)1-x(CuBiS2)x samples (Fig. 6b) exhibit positive values, indicating p-type conductivity consistent with Hall measurements. It is found that all CuBiS2 alloyed samples exhibit significantly enhanced S among the whole temperature range. S at 823 K increases from ~133 μV K−1 for the pure GeTe to ~240 μV K−1 for the (GeTe)0.93(CuBiS2)0.07 sample, exhibiting great advantages compared with other reported state-of-the-art GeTe based systems (Supplementary Fig. 6)17,29,32,47–49. In order to elucidate the mechanism of large increase of the Seebeck coefficient of GeTe, the Pisarenko relation between S and the carrier concentration (n) is calculated based on the single parabolic band (SPB) model. The density-of-state (DOS) effective mass m* is fitted by SPB model in Supplementary Table 5. All the CuBiS2 alloying samples lie above the m*=1.6 m0 line, and the m* improves with the increasing alloying content of CuBiS2 from 1.03 m0 for pure GeTe to 2.23 m0 for (GeTe)0.93(CuBiS2)0.07 sample. Previously reported data of GeTe-CuSbSe2 28, GeTe-CuBiSe2 29, and GeTe-NaSbTe2 31 are also included for comparison in Fig. 6d. The (GeTe)1-x(CuBiS2)x samples exhibit higher m* as compared to these alloying systems. The large enhancement of m* clearly predicts that CuBiS2 alloying modifies the electronic band structures of GeTe.

To decode the mechanism of higher m* of (GeTe)1-x(CuBiS2)x alloying systems and understand the effects of CuBiS2 alloying on the band structures of GeTe, we carrier out Density-functional theory (DFT) calculation of pure GeTe and (GeTe)0.93(CuBiS2)0.07 in the cubic phase. The supercell used for calculating is shown in Supplementary Fig. 7. The k-point paths in the first Brillouin zone used for band structure calculations are shown in Supplementary Fig. 8. For the pristine GeTe compound (Fig. 6g), it exhibits the direct band gap (Eg=0.35 eV) semiconductor with the valence band maximum (VBM or VBM1 in Fig. 6g) and conduction band minimum (CBM) at the L point in the Brillouin zone (BZ). The second and third valence band maxima (VBM2 and VBM3) are located at the Σ point and along the Γ-X direction, respectively. The valley degeneracy (Nv) of VBM1 (at the L point), VBM2 (at the Σ point), and VBM3 (along the Γ-X direction) are 4, 12, and 6, respectively. For the band offsets of these valence band maxima, which are related to the Seebeck coefficients of samples, we notice that the energy difference between the VBM1 and VBM2 (ΔEVBM1-VBM2) is 67 meV. However, ΔEVBM1-VBM3 is quite large, 273 meV. Such large band offsets can hardly be recognized as the band convergency. Once the CuBiS2 is alloyed in GeTe (Ge63Cu6Bi6Te63S12), the electronic band structures are significantly changed (Fig. 6h). Interestingly, under the doping, the compound is changed to an indirect band gap semiconductor: the valence band maximum (VBM) is shift from the L point (the VBM1 position) to the Σ point (the VBM2 position) and the band gap is slightly enlarged to 0.49 eV. Obviously, by shifting the VBM from the L point to the Σ point, the Nv is significantly increased from 4 to 12. Additionally, CuBiS2 alloying clearly lifts the energy positions of VBM2 and VBM3, decreasing the band offset with respect to the VBM1 (Fig. 6h and Table 1): ΔEVBM1-VBM2 = −16 meV and ΔEVBM1-VBM3 = 63 meV (the negative band offset value of ΔEVBM1-VBM2 is due to the shift of VBM from VBM1 to VBM2). Thus, these small band offsets can be considered as the band alignment of VBM1, VBM2 and VBM3. Correspondingly, Nv is increased to an ultra-high value of 4 (NVBM1) + 12 (NVBM2) + 6 (NVBM3) = 22. In previous reported works, they focused on promoting valley degeneracy of L and Σ. Cd17, Ti50, Ca19, and Mn51 elements doping in GeTe are proved to realize the band convergency between L and Σ. However, the energy difference between light and heavy bands was not effectively eliminated, weakening the contribution of heavy bands. Thus, the actual contributing valley degeneracy ranges from 4 to 16. Then, a refined band alignment was realized in Zn-doped Ge1−xSbxTe and V-doped Ge1−xBi xTe samples18,42, band edges between Σ and L nearly locate at the same energy level (ΔEVBM1-VBM2 ≤ 0.01 eV), leading to a total valley degeneracy of 16 (NVBM1=4, NVBM2=12). However, from the band structures of c-GeTe, we notice that there has the third valence band (VBM3, Nv=6) along the Γ-X direction, which is always ignored in former works. If we could reduce the energy difference between third valence band and VBM1, we can further increase the Nv and involve more channels for carrier transport. Therefore, by alloying CuBiS2 in GeTe, we enable the band alignment not only between the VBM1 and VBM2, but also between VBM1 and VBM3, which contribute to a total valley degeneracy of 22 (NVBM1=4, NVBM2=12, NVBM3=6). This is a much higher value than those of previous reported literature8,17–19,42,51 (Supplementary Table 6). Therefore, the CuBiS2 alloying induces VBM off the high-symmetry point in the BZ and the band alignment among the three valence band maxima, owing to the combined effect of CuBiS2 alloying43,52. Both of them lead to the large Nv and boost the electronic density of states (DOS) around the valence band maximum, which is clearly seen in Fig. 6i. The boosted DOS will induce the high DOS effective mass (m*) and the correspondingly large Seebeck coefficient. Moreover, increasing Nv is an effective way to enhance m* but avoiding deteriorating μ53, which is in good agreement with the experimental measurements.

CuBiS2 alloying contributes to a sharp increase of power factor (PF) throughout the measured temperature range, as presented in Fig. 6e. The room temperature PF increases from 6 μW cm-1 K-2 for the pure GeTe to 22 μW cm-1 K-2 for (GeTe)0.93(CuBiS2)0.07 sample. It is worth noting that a remarkable PF of ~49 μW cm-1 K-2 is achieved in the (GeTe)0.93(CuBiS2)0.07 sample at 673 K due to markedly improved S.

The power factor shows a significant degradation (Supplementary Fig. 9) as CuBiS2 content further increases to x=0.09. As CuBiS2 alloying content exceeds the solid solubility limit, CuBiS2 precipitates presents within the matrix. These precipitates cause strong carrier scattering, resulting in a sharp deterioration of electrical transport performance. The comparison of the PF for (GeTe)0.93(CuBiS2)0.07 sample with other reported GeTe materials is shown in Supplementary Fig. 10, 29, 41, 54–57. The large integral area of PF demonstrates that CuBiS2 alloying enhances electrical transport properties of GeTe over the whole temperature range, making it promising to achieve high wide-temperature-range thermoelectric performance. The weighted mobility (μw) in Fig. 6f provides a direct assessment of the intrinsic electrical transport characteristics. Details of the calculation can be found in Supporting Information. μw exhibits a declining trend with rising temperature, which can be attributed to intensified carrier scattering caused by impurities. Notably, the (GeTe)0.93(CuBiS2)0.07 sample possess significantly higher μw than pristine GeTe and demonstrates the highest μw among investigated samples, indicating its superior electrical transport characteristics compared to its counterparts.

ZT values, energy conversion efficiency of the thermoelectric device, and mechanical properties of (GeTe)1-x(CuBiS2)x samples
ZT value of (GeTe)1-x(CuBiS2)x samples shows pronounced enhancement compared to pristine GeTe (Fig. 7a). An extraordinary peak ZT of ~2.5 at 723 K is achieved in (GeTe)0.93(CuBiS2)0.07, which benefits from the synergistic optimization of thermal and electrical performance enabled by CuBiS2 alloying. This high thermoelectric performance surpasses most of promising reported GeTe based thermoelectric materials (Supplementary Fig. 11)29, 38, 58–62. Repeated measurements in Supplementary Fig. 12 demonstrate good experimental reproducibility for such high performance. Moreover, the material maintains its thermoelectric performance after heating-cooling cycles, demonstrating excellent thermal stability (Supplementary Fig. 13). XRD measurements (Supplementary Fig. 14) reveal that the sample maintained consistent phase components before and after cycling thermoelectric measurements. Thermogravimetric analysis (TGA) results (Supplementary Fig. 15) reveal negligible weight loss after heating, confirming that elemental volatilization is negligible during heating. SEM and EDS analysis proves that the sample did not significantly degrade under high temperatures (Supplementary Fig. 16).

Attaining a high average ZT across a broad temperature range is greatly desirable for promoting the practical application of GeTe because thermoelectric devices need to operate over the several-hundred-kelvin operating range. It is worth noting that ZT is significantly enhanced in the whole temperature range (Supplementary Fig. 17) due to significantly enhanced PF and sharply reduced lattice thermal conductivity22,29,38,55,58,60,63. A record-high ZT (average ZT) of 1.9 was realized between 400 and 823 K. The wide-temperature-range thermoelectric performance outperforms most state-of-the-art p-type thermoelectric materials64–68, enabling this GeTe-based alloy as one of the best medium-temperature thermoelectric materials. The ZTave value of the (GeTe)0.93(CuBiS2)0.07 sample is 442% higher than that of pure GeTe and outperforms utmost GeTe-based systems, as shown in Fig. 7b. A (GeTe)0.93(CuBiS2)0.07 single leg device was fabricated to demonstrate the application potential. The output voltage (V), output power (P), and energy conversion efficiency (η) as functions of electric current (I) are shown in Fig. 7c, d and Supplementary Fig. 18. Experimentally, we achieved a high output power of 54 mW and a corresponding η of ~12% under a temperature difference (ΔT) of 470 K. The maximum efficiency outperforms most of the reported high-performance thermoelectrics, including those of SnSe69, PbTe70, Half-Heusler71, BiSbTe72, PbSe73 and GeTe systems29,40,74,75 (Supplementary Fig. 19). Except for superior thermoelectric performance, robust mechanical properties of GeTe materials are also important for practical applications. Vickers indentation method was used to measure the micro-Vickers hardness of (GeTe)1-x(CuBiS2)x samples. The hardness of the samples keeps rising with the increasing alloying content of CuBiS2 in Fig. 7e. Especially, the best performance (GeTe)0.93(CuBiS2)0.07 sample achieved a hardness of ~224 Hv, which is ~93% higher than that of the pure GeTe (~116 Hv). This result also exhibits great advantages compared to the other reported works45,61,76. Moreover, the compressive strain-stress of the (GeTe)0.93(CuBiS2)0.07 sample is tested and shown in Fig. 7f. (GeTe)0.93(CuBiS2)0.07 sample exhibits enhanced compressive strengths of 349 MPa, which is much higher than utmost reported GeTe thermoelectrics77–79. It is worth noting that the compressive strength of (GeTe)0.93(CuBiS2)0.07 sample also exhibits superiority to other typical thermoelectric systems30,80,81. Both dramatically improved hardness and compressive strength can be accounted for by the presence of abundant nanotwins in the matrix. The presence of nanoscale twin boundaries in GeTe effectively provides adequate barriers to block dislocation motion (shown in Supplementary Fig. 20)31. Additionally, dislocations can be pinned at the nanoscale twin boundary and react with other dislocation to form a stable, immobile dislocation lock82. These factors result in a hardening effect. Therefore, the mechanical properties of hardness and compressive strength for (GeTe)0.93(CuBiS2)0.07 sample can be both markedly improved. The enhanced mechanical properties extend the potential of GeTe-based materials to serve as a reliable and long-life thermoelectric device. In summary, we demonstrated that high thermoelectric performance and mechanical properties are simultaneously achieved in CuBiS2 alloyed GeTe through nanotwin architecture and inducing ultra-high valley degeneracy. Microstructural observations reveal that dense nanotwins and ordered vacancy arrays are present in the GeTe matrix. The architecture of dense nanotwins, along with ordered vacancy arrays and point defects, leads to significantly reduced lattice thermal conductivity. Furthermore, CuBiS2 alloying resulted in refined valence band alignment, which increases the Nv to an ultra-high value of 22 and produces a sharp increase in power factor over the whole temperature range. Consequently, synergistically optimized electron and phonon transport properties contribute to a high peak ZT value of 2.5 and a record-high average ZT of 1.9 in the (GeTe)0.93(CuBiS2)0.07 sample. Moreover, hardness and compressive strength are greatly enhanced due to the block of dislocation slip by dense nanotwins, which is beneficial for the assembly and application of thermoelectric devices.

Methods
Sample Synthesis
Polycrystalline (GeTe)1-x(CuBiS2)x samples are synthesized by the vacuum melting method. High-purity raw materials of Ge (99.99%), Cu (99.99%), Bi (99.99%), Te (99.99%), and S (99%) powders are weighed according to the nominal compositions. The raw powders were thoroughly blended before loading into quartz tubes. These tubes were evacuated to high vacuum and hermetically sealed using a high-temperature torch. Subsequent thermal treatment involved heating the samples in a muffle furnace, holding them isothermally at 1273 K for 8 hours, followed by rapid ice water quenching. The samples achieved then underwent a 3-day annealing process at 923 K. The resulting ingots were manually pulverized using a mortar and pestle to obtain fine powders. These powders were loaded into 13-mm-diameter graphite dies and sintered into high relative density cylindrical samples under a uniaxial pressure of 50 MPa using a LABOX-110h system in vacuum. These yielded samples are in dimensions of 13 mm in diameter and 10 mm in height.

Material characterization
The crystal structure and phase information analysis of the powder samples are supported by (XRD) Bruker D8 Advance instrument with Kα radiation (λ=0.154060 nm). DSC analysis was conducted using a Mettler Toledo TGA/DSC 3+ instrument at a heating rate of 20 K/min under a nitrogen atmosphere to detect the phase transition temperature. The scanning electron microscopy (SEM) (FEI Quanta 250 FEG) equipped with the energy dispersive spectrometry (EDS) (Inca, Oxford instruments) was performed on the microstructure investigation of the samples. Micrographs were acquired primarily using the Secondary Electron Detector (SED) at an acceleration voltage of 20 kV, a beam condition set to a spot size of 3.0, and a working distance of 10 mm to optimize both image contrast and EDS signal. JEOL JEM-ARM300F2 aberration-corrected scanning transmission electron microscope (STEM) operated at an acceleration voltage of 300 kV. The STEM imaging was conducted with a probe size of approximately 8c, a convergence semi-angle of about 25 mrad, and collection angles ranging from 90 to 370 mrad. Samples for STEM observation were prepared by mechanical grinding followed by ion milling (GATAN 691). The thinning procedure consisted of two stages: an initial coarse thinning at a higher voltage (4–5 kV), followed by a final precision polishing at a lower voltage (1–2 kV) to obtain an electron-transparent area free. Both Seebeck coefficient and electrical conductivity were characterized using an Ulvac-Riko ZEM-3 system under a helium atmosphere from 300–823 K. The total thermal conductivity κ was calculated from the equation: κ=λdCp. Thermal diffusivity was measured directly via the laser flash technique on a Netzsch LFA457 instrument. The specific heat capacity (Cp) was calculated used Dulong-Petit limit (Supplementary Fig. 21). The density (d) of samples was determined by a density meter using the Archimedes method. The uncertainties for the electrical conductivity and Seebeck coefficient measurements are both 5%. The uncertainty for the total thermal conductivity is about 12% (comprising uncertainties of 5% for the thermal diffusivity, 5% for the specific heat, and 2% for the density). The combined uncertainty for all measurements involved in the calculation of the ZT is approximately 20%. The Hall carrier concentration (n) and carrier mobility (μ) were calculated from the formulas n=1/eRH and μ=RH/ρ, respectively. The Hall coefficients (RH) were measured by the van der Pauw method on the Hall-effect measurements system (Ecopia HMS-3000) at room temperature. Vickers hardness measurements were performed using an HVS-1000 instrument, applying a load of 1 N for a dwell time of 10 seconds to ensure measurement accuracy. Compressive strength was tested on an Instron 7648 machine with a loading rate of 0.05 mm/min.

Theoretical calculations
We use the projected augmented wave (PAW)83 scheme with the generalized gradient approximation of Perdew-Burke-Ernzerhof (PBE)84 for the electronic exchange-correlation functional in the Vienna ab initio simulation package (VASP). A cutoff energy of 450 eV is applied for the plane wave expansion, and the Monkhorst-Pack85 approach is used to sample the Brillouin zones with a roughly constant density of k-points (30 Å3). The structures are fully optimized until the maximum force on each atom is below 0.01 eV. To simulate the experimentally suggested GeTe alloying with CuBiS2, we perform the special quasi-random structures (SQS)86,87 method in the Alloy Theoretic Automated Toolkit (ATAT) code. This method can be used to construct the solid solution structure or randomly occupy the lattice during doping. Under this approximation, 8% Cu+8% Bi and 16% S are randomly doped at the Ge and Te sites in the cubic GeTe phase (Ge63Cu6Bi6Te63S12, Supplementary Fig. 7b). To compare the band structures with or without dopants, the band unfolding method (the BandUP code)88 is used to unfold the SQS supercell band structure into the primitive Brillouin zone of the pristine GeTe compound.

Thermoelectric device fabrication and characterization
The thermoelectric single-leg module was fabricated by first sintering the material via SPS, then cutting it into a block measuring 2.95 × 3.07 × 14.2 mm3, and finally soldering it between two copper plates using a commercial Sn64Bi35Ag1 solder. The soldering process was conducted in a glove box, where a hot plate and a heater block were employed to simultaneously heat both ends of the leg. Subsequently, the device's electrical power output and conversion efficiency were measured using a home-built test system. More details were given in previously reported work22.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Li et al. reports CuBiS2 alloyed GeTe-based Thermoelectric Materials with a high peak ZT of 2.5 as well as an exceptional average ZT of 1.9 through nanotwin architecture and inducing ultra-high valley degeneracy. DFT calculations reveal that CuBiS2 alloying realizes refined valence band alignment in GeTe, generating an ultra-high valley degeneracy of 22. Although the reported zT values are comparable to typical GeTe performance, the mechanism by which CuBiS2 alloying induces valence-band alignment needs further validation. Given the chemical incompatibility between CuBiS2 and GeTe, its realistic solubility and incorporation into the GeTe matrix remains uncertain. Moreover, several issues relating to claims as enlisted below require major revision.\n1. How do chemical incompatibility issues of incorporating CuBiS2 (a sulfide compound) into GeTe (telluride matrix), by alloying affect the overall phase stability? Moreover, discussion relating to solubility and its limits needs further clarification.\n2. The observed increase in lattice parameter (Figure 2d) requires a more rigorous explanation, including how Cu, Bi, and S atoms occupy lattice sites in GeTe, especially given the possibility of structural phase transitions. Furthermore, the phase constitution and quantitative phase fractions present in the alloyed samples are not adequately established/clarified.\n3. With valley degeneracy as high as 22, very large effective mass is likely. How does it vary in comparison to previous reports and theoretical evaluation ? Moreover, the physical origin and its compatibility with the expected band symmetry require more detailed justification.\n4. Figure 6(e) indicates increasing power factor with increasing CuBiS2 content. Why is higher content not explored ?\n5. Discuss thermal stability and temperature dependent heat capacity of the samples. Particularly, how does CuBiS2 alloying and nanotwin architecture affect the specific heat capacity of the GeTe.?\n6. A comparative analysis with respect to published studies on GeTe may be included to better comprehend the relevance of ultra-high valley degeneracy.\n7. To what extent does the observed enhancement in zT translate into an actual improvement in overall energy conversion efficiency? Presenting device-level efficiency measurements would strengthen and substantiate the claims of high thermoelectric performance.\n8. Comment on the measurement error. Similarly, discuss the propagation errors and their impact on the accuracy of the ZT measurements for the synthesized alloys.\n9. There are prevailing typos and errors which need to be thoroughly checked and corrected.", "reviewer_2": "Dear Editor,\nI have reviewed the manuscript “Nanotwin Architecture and Ultra-high Valley Degeneracy Lead to High Thermoelectric Performance in GeTe-based Thermoelectric Materials” and recommend its publication after revision. Below I provide my detailed comments for the editor and the authors.\nWhat are the noteworthy results?\nThe authors demonstrate experimentally that alloying GeTe with Cu, Bi, and S enhances the power factor and reduces the lattice thermal conductivity, increasing the average zT over the relevant temperature range from 0.4 to 1.9. They attribute these improvements to a combination of nanostructuring (twin boundaries, vacancy arrays, and point defects generated by alloying), which lowers the lattice thermal conductivity, together with band structure optimization induced by alloying, which enhances the power factor.\nIs the work significant?\nThis work combines several strategies to enhance thermoelectric performance, provides a reasonable explanation of the observed trends, and reaches a high average zT. The approach is relevant for the design of high-efficiency modules based on GeTe, and similar strategies could be transferred to other thermoelectric materials.\nDoes the work support the conclusions and claims, or is additional evidence needed?\nIn general, the conclusions are well supported by the data. There are, however, a few points that should be clarified or further discussed:\nHow were the point defect, grain boundary, and vacancy densities used in the Debye–Callaway model determined or estimated? Please specify the basis for these parameters and their uncertainty.\nAre the properties stable upon thermal cycling? Is there microstructure evolution when the samples are heated to the operating temperature (up to 800 K)? Defect densities and distributions might change when heat is applied. Adding information about that can help strengthen the article (e.g. a figure showing several heating–cooling cycles would help the reader understand whether this is an important effect).\nIn Figure 4e, f, i, and j the authors use HAADF contrast to comment on the distribution of alloying elements and vacancies. Not much can be seen in Figure 4e and f, and based on the distributions shown in Figure 4i and j it is difficult to conclude that Bi, Cu, and S substitute preferentially on specific lattice sites or to localize individual vacancies. I suggest softening these statements or supporting them with additional evidence (for example EDS/EELS mapping or simulations).\nIs the methodology sound?\nThe overall methodology appears sound, but some important experimental details are missing and should be provided to ensure reproducibility:\nFor SEM: specify detector type (SE or BSE), acceleration voltage, probe current (or beam conditions), and working distance.\nFor STEM: specify acceleration voltage, convergence semi-angle, collection angles for the HAADF and BF/ADF detectors, and the approximate probe size. Please also describe how the STEM samples were prepared (FIB, ion milling conditions, etc.).\nEDS is mentioned in both SEM and STEM, but no EDS data are shown. Either include representative EDS results or clarify how EDS was used and why the data are not shown.\nSmall comments\nLine 50: duplicated “potential”.\nLine 80: “secondary phases”.\nLine 106: I suggest adding a brief comparison of the obtained average zT values with state-of-the-art GeTe-based thermoelectrics.\nLine 163: “magnified” instead of “further amplified”.\nLine 171 and 180: Figure 3 is referenced incorrectly.\nLine 190: likely also references a wrong figure, please check.\nLine 218: Figure 3 is introduced after Figure 4; consider reordering or adjusting the text.\nBest regards,"}, "author_response": "Thank you for your careful review and the insightful suggestions offered to improve our manuscript. We have provided a point-by-point response to your comments below. We hope the revisions made to the manuscript adequately address your concerns and significantly improve the quality of this work.\nComment 1: How do chemical incompatibility issues of incorporating CuBiS (a sulfide compound) into GeTe (telluride matrix), by alloying affect the overall phase stability? Moreover, discussion relating to solubility and its limits needs further clarification.\nResponse:\nThanks for your comments. Except for a small amount of Ge precipitates, no obvious impurity phase can be detected in the XRD pattern of (GeTe) (CuBiS ) samples 1-x 2 x (Fig. R1) as CuBiS alloying content x ≤ 0.07. This indicates that the CuBiS can be 2 2 well dissolved into the GeTe matrix. In order to further investigate the distribution of Cu, Bi, and S elements within the GeTe matrix, we performed SEM and corresponding EDS analysis in Fig. R2. It is clearly found that the Cu, Bi, and S elements are homogeneous distribution in the GeTe matrix. This indicates good chemical compatibility of CuBiS with GeTe. 2\nIn order to investigate solid solubility of CuBiS , we prepared the sample with 2 higher CuBiS alloying content of x = 0.09 during revision. In the XRD pattern of (GeTe) (CuBiS ) sample (Fig. R1), distinct diffraction peaks indexed to the 0.91 2 0.09 secondary phase of CuBiS were observed. This suggests that the solubility limit of 2 CuBiS in GeTe is lower than 9%.\nFig. R2. SEM images of the polished surface of the (GeTe) (CuBiS ) sample. 0.93 2 0.07 and corresponding Elemental mapping.\nRevisions: We have added the discussion on page 6.\n\"As the CuBiS alloying content reaches x = 0.09, distinct diffraction peaks indexed 2 to the secondary phase of CuBiS were observed. This suggests that the solubility 2 limit of CuBiS in GeTe is lower than 9%.\"\nResponse:\nThank you for your constructive suggestion. The lattice constant a and b increase with increasing CuBiS content, which can be attributed to the fact that the ionic radii of 2 both Bi3+ (1.03 Å) and Cu+ (0.77 Å) are larger than that of Ge2+ (0.73 Å). Rietveld refinement details of the XRD pattern of (GeTe) (CuBiS ) sample are shown in 0.93 2 0.07 Fig. R3 and Table R1. The XRD patterns of the (GeTe) (CuBiS ) sample can be 0.93 2 0.07 well fitted by the r-GeTe structure with a space group of R3m (160), similar to the parent GeTe phase. Based on our Rietveld refinement, the Cu and Bi atoms occupy the Ge site (Wyckoff position 2c) with coordinates of (0, 0, 0.2437), while the S occupy Te site (Wyckoff position 2c) with coordinates of (0, 0, 0.7629).\nThe phase constitution and quantitative phase fractions present in the alloyed samples are analyzed, as shown in Table R2. It indicates good dissolution of CuBiS 2 in GeTe when alloying content is less than or equal to x = 0.07.\nFig. R3. Rietveld refinement details of (GeTe) (CuBiS ) sample. 0.93 2 0.07\nTable R1. Rietveld refinement details of the (GeTe) (CuBiS ) sample. 0.93 2 0.07\nWyckoff position Atom Occupancy x y z\nGe 0.8856 0.0000 0.0000 0.2437\nCu 0.0596\nBi 0.0548\nTe 0.8819 0.0000 0.0000 0.7629\nS 0.1181\nTable R2. Quantitative phase fractions extracted from the XRD Rietveld refinement for (GeTe) (CuBiS ) samples. 1-x 2 x\nPhase fraction (%) Composition GeTe Ge CuBiS 2\nGeTe 100 / /\n(GeTe) (CuBiS ) 100 / /\n0.97 2 0.03\n(GeTe) (CuBiS ) 100 / /\n0.95 2 0.05\n(GeTe) (CuBiS ) 99.73 0.27 /\n0.93 2 0.07\n(GeTe) (CuBiS ) 97.85 0.46 1.69\n0.91 2 0.09\nRevisions: We have added Table R1 and Table R2 as Table S1 and Table S2 to the supporting information. Related discussion was included into the revised manuscript of page 6-7.\n\"Rietveld refined XRD patterns and the refinement details can be found in Fig. 2c-2d and Fig. S1, respectively. Fig. 2d clearly show that the lattice constant a and b increase from 4.16 Å to 4.20 Å with increasing CuBiS alloying content, which can be 2 attributed to the fact that the ionic radii of Bi3+ (1.03 Å) and Cu+ (0.77 Å) are both larger than that of Ge2+ (0.73 Å). The occupied positions of the corrected atoms are exhibited in Table S1. It is found that the Cu and Bi atoms occupy the Ge site (Wyckoff position 2c) with coordinates of (0, 0, 0.2437), while the S occupy Te site (Wyckoff position 2c) with coordinates of (0, 0, 0.7629). Furthermore, the phase constitution and quantitative phase fractions present in the alloyed samples are clarified (Table S2). It proves the good dissolution of CuBiS in GeTe when alloying 2 content is less than or equal to x = 0.07. Because the phase transition progress from r-GeTe to c-GeTe is caused by center cation atom shifting along the [111] direction (Peierls distortion), we can use the lattice angle α to represent the lattice symmetry10.\"\nComment 3: With valley degeneracy as high as 22, very large effective mass is likely. How does it vary in comparison to previous reports and theoretical evaluation? Moreover, the physical origin and its compatibility with the expected band symmetry require more detailed justification.\nResponse:\nThank you for your comment. For the pristine cubic GeTe phase (c-GeTe), its valence band maximum (VBM, or VBM1 in our manuscript) is at the L point in the Brillouin zone (BZ). From the shape of the BZ, we can recognize that its valley degeneracy (N ) v is 4. Moreover, the second valence band (VBM2) at the Σ point is ~67 meV lower than the VBM, and its N =12.1 Since enhancing the band convergency plays an v essential role in boosting the Seebeck coefficient, many works were dedicated to degenerating the two bands of VBM1 (at L) and VBM2 (at Σ) in GeTe. For example, Cd,2 Ti,3 Ca,4 and Mn5 elements doping in GeTe are proved to realize the band convergency between L and Σ. However, the energy difference between light and heavy bands was not effectively eliminated, weaking the contribution of heavy bands. Thus, the actual contributing valley degeneracy ranges from 4 to 16. Then, a refine band alignment was realized in Zn-doped Ge Sb Te and V-doped Ge Bi Te 1−x x 1-x x samples,6, 7 band edges between L and Σ nearly locate at the same energy level (EVBM1-VBM2 ≤ 0.01 eV ), leading to a total band degeneracy of 16 (N =4, v N =12). VBM1 v VBMI2n previous reported works, they focused on promoting band degeneracy of L and Σ. However, from the band structures of c-GeTe, we notice that there has the third valence band (VBM3, N =6) along the -X direction, which is always ignored in V former works. If we could reduce the energy difference between third valence band and VBM1, we can further increase the band degeneracy (N ) and involve more v channels for carrier transport. Therefore, by alloying CuBiS in GeTe, we enable the 2 band alignment not only between the VBM1 and VBM2, but also between VBM1 and VBM3 (along the -X). In other words, we successfully achieve the band convergency of three valence bands (VBM1, VBM2 and VBM3), which contribute to a total band degeneracy of 22 (N =4, N =12, N = 6). This is a much v v v higher value than those of previoVuBsM 1reportedV lBiMte2rature (TaVbBlMe 3R3). The theoretically calculated band degeneracy conforms to the band symmetry criteria. The third valence band that realized degenerate after CuBiS alloying is located along the Γ–X k-point 2 path in the first Brillouin zone, possessing six complete Fermi surface pockets.\nTable R3. The Band degeneracy (N ) realized in typical GeTe-based thermoelectric v materials of c-GeTe structure.\nMaterial Contribution Total degeneracy\nc-GeTe8 =4 <12 < 16\nGe Ca Sb Te4 VBM1 =4 VBM2 <12 < 16\n0.85 0.05 0.1 N v N v\nGe Cd Bi Te2 VBM1 =4 VBM2 <12 < 16\n0.88 0.05 0.07 N v N v\nGe Mn Sb Te5 VBM1 =4 VBM2 <12 < 16\n0.86 0.10 0.04 N v N v\nGe Sb Zn Te7 VBM1 =4 VBM2 =12 16\n0.86 0.1 0.04 N v N v\nGe V Bi Te6 VBM1 =4 VBM2 =12 16\n0.9 0.02 0.08 N v N v\nThis work VBM1 =4 VBM2 =12 =6 22\nN v N v\nVBM1 VBM2 VBM3\nN v N v N v\nRevision: Table R3 was included into the supporting information (Table S6). Related discussion was included into the revised manuscript.\n\"In previous reported works, they focused on promoting band degeneracy of L and Σ. Cd17, Ti50, Ca19, and Mn51 elements doping in GeTe are proved to realize the band convergency between L and Σ. However, the energy difference between light and heavy bands was not effectively eliminated, weaking the contribution of heavy bands. Thus, the actual contributing valley degeneracy ranges from 4 to 16. Then, a refine band alignment was realized in Zn-doped Ge Sb Te and V-doped Ge Bi Te 1−x x 1-x x samples18, 42, band edges between Σ and L nearly locate at the same energy level (EVBM1-VBM2 ≤ 0.01 eV), leading to a total band degeneracy of 16 (N =4, v N =12). However, from the band structures of c-GeTe, we notice that VthBeMr1e has v thVeB Mth2ird valence band (VBM3, N =6) along the -X direction, which is always V ignored in former works. If we could reduce the energy difference between third valence band and VBM1, we can further increase the band degeneracy (N ) and v involve more channels for carrier transport. Therefore, by alloying CuBiS in GeTe, 2 we enable the band alignment not only between the VBM1 and VBM2, but also between VBM1 and VBM3, which contribute to a total band degeneracy of 22 (N v =4, N =12, N = 6). This is a much higher value than those of prevViBoMu1s v v reporteVdB Mli2terature8, 1V7B-1M9, 342, 51 (Table S6).\"\nComment 4: Figure 6(e) indicates increasing power factor with increasing CuBiS2 content. Why is higher content not explored?\nResponse:\nThanks for your suggestions. GeTe with higher CuBiS alloying content (x=0.09) was 2 prepared during revision. We measured electrical transport properties of the sample with x=0.09, as shown in Fig. R4. Our results reveal that the power factor shows a significant degradation as CuBiS content further increases to x = 0.09. As CuBiS 2 2 alloying content exceeds the solid solubility limit, CuBiS precipitates presents within 2 the matrix. These precipitates cause strong carrier scattering, resulting in a sharp deterioration of electrical transport performance. We have added Fig. R4 to Fig. S9 in the supporting information. The related discussion was incorporated into revised manuscript\na b c\nFig. R4. Temperature-dependent power factor (PF) of (GeTe) (CuBiS ) samples. 1-x 2 x\nRevisions:\n\"The power factor shows a significant degradation (Fig. S9) as CuBiS content further 2 increases to x = 0.09. As CuBiS alloying content exceeds the solid solubility limit, 2 CuBiS precipitates presents within the matrix. These precipitates cause strong carrier 2 scattering, resulting in a sharp deterioration of electrical transport performance.\"\nComment 5: Discuss thermal stability and temperature dependent heat capacity of the samples. Particularly, how does CuBiS2 alloying and nanotwin architecture affect the specific heat capacity of the GeTe.?\nResponse:\nThanks for your constructive suggestions. We conducted a detailed investigation on thermal stability of (GeTe) (CuBiS ) during revision. Firstly, thermogravimetric 1-x 2 x analysis (TGA) was performed to assess the thermal stability of (GeTe) (CuBiS ) 0.93 2 0.07 material (Fig. R5), and the results indicated negligible weight loss over a wide temperature range, confirming that elemental volatilization is negligible during heating. Then, heating and cooling cycle measurements were carried out on high performance sample. An almost negligibly small hysteresis is found, suggesting that the material maintains its thermoelectric performance after heating-cooling cycles (Fig. R6). Finally, we measured XRD for high performance (GeTe) (CuBiS ) 0.93 2 0.07 sample before and after cycling thermoelectric measurements, as shown in Fig. R7. The sample maintained consistent phase components before and after cycling thermoelectric measurements. These results demonstrate good thermal stability of the CuBiS alloying sample. 2\nFig. R5. Thermogravimetric analysis for pure GeTe and (GeTe) (CuBiS ) 0.93 2 0.07 sample.\n(a) (b)\n(GeTe) (CuBiS)\n0.93 20.07\n(c) (d)\nFig. R6. The heating-cooling cycling measurement of the high thermoelectric performance (GeTe) (CuBiS ) sample. (a) Electrical conductivity, (b) Seebeck 0.93 2 0.07 coefficient, (c) Thermal conductivity, (d) ZT.\nFig. R7. XRD patterns of (GeTe) (CuBiS ) sample before and after 0.93 2 0.07 heating-cooling cycling measurement.\nTo investigate the effect of CuBiS alloying and nanotwin architecture on the 2 heat capacity (C ) for the pure GeTe and (GeTe) (CuBiS ) sample, we measured p 0.93 2 0.07 the C under different heating rates by DSC (Fig. R8). It is found that the C decreases p p after CuBiS alloying as compared with pure GeTe. The measured heat capacity of 2 (GeTe) (CuBiS ) sample is close to Dulong-Petit limit at temperatures not close 0.93 2 0.07 to that of phase transition. Most literatures reported high performance GeTe thermoelectrics used Dulong-Petit limit for calculating heat capacity.7, 9, 10 To have a consistent comparison on thermal conductivity and ZT of GeTe thermoelectrics, it is therefore meaningful to show the transport property with a heat capacity of Dulong Petit limit as well in this work.\nFig. R8. Heat capacity of (GeTe) (CuBiS ) samples by DSC measurements, 1-x 2 x indicating the Dulong-Petit limit as an effective approximation.\nRevision: We have added Fig. R6, Fig. R7, Fig. R5 and Fig. R8 as Fig. S13, Fig. S14, Fig. S15, and Fig. S21 in the supporting information. The corresponding discussion was included into the revised manuscript.\n\"Moreover, the material maintains its thermoelectric performance after heating-cooling cycles, demonstrating excellent thermal stability (Fig. S13). XRD measurements (Fig. S14) reveal that the sample maintained consistent phase components before and after cycling thermoelectric measurements.\nThermogravimetric analysis (TGA) results (Fig. S15) reveal negligible weight loss after heating, confirming that elemental volatilization is negligible during heating.\nSEM and EDS analysis proves that the sample did not significantly degrade under high temperatures (Fig. S16).\"\nComment 6: A comparative analysis with respect to published studies on GeTe may be included to better comprehend the relevance of ultra-high valley degeneracy.\nResponse:\nThank you for your comment. Please see our Response to your Comment 3. In previous reported works, they focused on promoting band degeneracy between VBM1 (at L) and VBM2 (at Σ). However, from the band structures of c-GeTe, we notice that there has the third valence band (VBM3, N =6) along the -X direction, which is V always ignored in former works. By alloying CuBiS in GeTe, we enable the band 2 alignment not only between the VBM1 and VBM2, but also between VBM1 and VBM3 (along the -X). In other words, we successfully achieve the band convergency of three valence bands (VBM1, VBM2 and VBM3), which contribute to a total band degeneracy of 22 ((N =4, N =12, N = 6). This is a much v v v higher value than those in the formVBeMr 1literatureVsB (MT2able R4). VBM3\nComment 7: To what extent does the observed enhancement in zT translate into an actual improvement in overall energy conversion efficiency? Presenting device-level efficiency measurements would strengthen and substantiate the claims of high thermoelectric performance.\nResponse:\nWe thank the reviewer for raising this insightful point regarding the translation of material ZT to device-level efficiency.\nWe have performed the single leg measurement for the (GeTe) (CuBiS ) 0.93 2 0.07 thermoelectric device during revision. The output voltage (V), output power P, and conversion efficiency ( as functions of electric current (I) are shown in Fig. R9 and ) Fig. R10c, d. Experimentally, we achieved a high output power of 54 mW under a temperature difference (ΔT) of 470 K. Eventually, the single leg possesses an outstanding energy conversion efficiency of ~12% with a ΔT of 470 K. The maximum efficiency outperforms most of the reported high-performance thermoelectrics, including those of SnSe11, PbTe12, Half-Heusler13, Bi Sb Te 14, PbSe15 and GeTe 0.4 1.6 3.2 systems16-19 (Fig. R11). The high energy conversion efficiency in (GeTe) (CuBiS ) device, proving its high thermoelectric performance. 0.93 2 0.07\nThe experimental efficiency is lower than theoretical conversion efficiency.\nDuring the efficiency measurement, thermal radiation significantly impacts the measured heat flow Q , which is difficult to measure accurately. As a result, the heat c flow through the device was overestimated and finally led to a lower actual efficiency. On the other hand, the soldering internal resistance of the single leg is much higher than the theoretical internal resistance due to the absence of a barrier material. The above reasons make the equipment efficiency lower than the theoretically calculated efficiency.\n(a) (b)\nFig. R9. Output voltage (U), input heat flow (Q) of the single leg (GeTe) (CuBiS ) thermoelectric device as functions of current (I) under various 0.93 2 0.07 temperature differences ( T).\na ∆ b\nc d\nh ~12%\nMAX\nDevice\ne f\nFig. R10. Dimensionless figure of merit ZT, conversion efficiency and mechanical properties. (a) Temperature-dependent ZT values of (GeTe) (CuBiS ) samples. (b) 1-x 2 x Comparing the average ZT (ZT ) in this study with those reported in other works. (c) ave Current (I) dependent output power (P), (d) energy conversion efficiency () of a single leg under various temperature differences (T). (e) The Vickers microhardness H of (GeTe) (CuBiS ) samples and comparison with data from literature. (f) The v 1-x 2 x compressive strain-stress and comparison with some typical TE materials.\nFig. R11. Comparison of measured thermoelectric conversion efficiencies for a (GeTe) (CuBiS ) single-leg device in this study and SnSe, PbTe, Half-Heusler, 0.93 2 0.07 Cu Se, Bi Sb Te , PbSe, GeTe systems among comparable temperature 2 0.4 1.6 3.2 differences T.\nRevision: We have added Fig. R9, Fig. R11 as Fig S18 and Fig S19 to the supporting information. We have added Fig. R10 as Fig. 7 in the manuscript. We have involved the corresponding discussion on page 18.\n\"A (GeTe) (CuBiS ) single leg device was fabricated to demonstrate the 0.93 2 0.07 application potential. The output voltage (V), output power P, and energy conversion efficiency () as functions of electric current (I) are shown in Fig. 7c, d and Fig. S18. Experimentally, we achieved a high output power of 54 mW and an outstanding of ~12% under a temperature difference ΔT of 470 K. The maximum efficiency outperforms most of the reported high-performance thermoelectrics, including those of SnSe68, PbTe70, Half-Heusler71, Bi Sb Te 72, PbSe73 and GeTe systems29, 40, 74, 75 0.4 1.6 3.2 (Fig. S19).\"\nComment 8: Comment on the measurement error. Similarly, discuss the propagation errors and their impact on the accuracy of the ZT measurements for the synthesized alloys.\nResponse:\nWe express our appreciation for the valuable suggestion provided. The uncertainties for the electrical conductivity and the Seebeck coefficient measurements are both equal to 5%. The uncertainty for the total thermal conductivity is about 12% (comprising uncertainties of 5% for the thermal diffusivity, 5% for the specific heat, and 2% for the density). The combined uncertainty for all measurements involved in the calculation of the ZT is approximately 20%.\nRevisions:\n\"The uncertainties for the electrical conductivity and the Seebeck coefficient measurements are both equal to 5%. The uncertainty for the total thermal conductivity is about 12% (comprising uncertainties of 5% for the thermal diffusivity, 5% for the specific heat, and 2% for the density). The combined uncertainty for all measurements involved in the calculation of the ZT is approximately 20%.\"\nComment 9: There are prevailing typos and errors which need to be thoroughly checked and corrected.\nResponse:\nThank you for your suggestion. We have carefully checked the whole content and corrected the typos and errors.\nReviewer #2\nComment:\nDear Editor,\nI have reviewed the manuscript “Nanotwin Architecture and Ultra-high Valley Degeneracy Lead to High Thermoelectric Performance in GeTe-based Thermoelectric Materials” and recommend its publication after revision. Below I provide my detailed comments for the editor and the authors.\nWhat are the noteworthy results?\nThe authors demonstrate experimentally that alloying GeTe with Cu, Bi, and S enhances the power factor and reduces the lattice thermal conductivity, increasing the average zT over the relevant temperature range from 0.4 to 1.9. They attribute these improvements to a combination of nanostructuring (twin boundaries, vacancy arrays, and point defects generated by alloying), which lowers the lattice thermal conductivity, together with band structure optimization induced by alloying, which enhances the power factor.\nIs the work significant?\nThis work combines several strategies to enhance thermoelectric performance, provides a reasonable explanation of the observed trends, and reaches a high average zT. The approach is relevant for the design of high-efficiency modules based on GeTe, and similar strategies could be transferred to other thermoelectric materials.\nDoes the work support the conclusions and claims, or is additional evidence needed?\nIn general, the conclusions are well supported by the data. There are, however, a few points that should be clarified or further discussed:\nResponse:\nWe appreciate your positive and encouraging comments. We have provided a point-by-point response below and have revised the manuscript according to your suggestions.\nComment 1: How were the point defect, grain boundary, and vacancy densities used in the Debye–Callaway model determined or estimated? Please specify the basis for these parameters and their uncertainty.\nResponse:\nThank you for your constructive suggestions.\nFor point defect: Due to the alloying of CuBiS with GeTe, we need to consider the 2 introduction of point defects by Cu, Bi, and S atoms. We calculated the contribution of impurity atoms according to the nominal composition of best performance (GeTe) (CuBiS ) sample. 0.93 2 0.07\nThe parameter Γ (Γ = Γ Γ ) describes the mass and atomic size contrast with the M + S lattice and represents the strength of point defect phonon scatterings, which includes two components, the scattering parameters due to mass fluctuations Γ and strain M field fluctuations Γ .\nS\n2\n𝑀𝑖 −𝑀̅\n𝛤𝑀 = 𝑥(1−𝑥)( )\n𝑀̅\n2\n𝑎𝑖 −𝑎̅\nis the average atom\n𝛤\ni𝑆c\n=\nm\n𝑥\na\n(\ns\n1\ns,\n− 𝑥) 𝜀\nis\n(\nthe a\n) \nerage atomic radius, ε is the\n𝑎̅\nphenomenological parameter.\n𝑀̅ 𝑎̅\nFor grain boundary: The average grain size (l) in the GeTe matrix after SPS sintering was determined to be approximately ~5 μm by statistical analysis of the polished surface using scanning electron microscopy (SEM). The average twin structure (d) size is estimated by transmission electron microscope (TEM) analysis to be ~90 nm. The uncertainty is dominated by the statistical distribution of sizes. We estimate 5% uncertainty in l and 5% uncertainty in d due to the limited sampling area in SEM and TEM.\nFor vacancy densities: Since Ge vacancy arrays have been demonstrated to form through the absence of a layer of Ge atoms, they are categorized as stacking faults to account for their contribution to phonon scattering. The defect density (N ) was va estimated through TEM analysis by counting the number of vacancy arrays intersecting per unit length as ~ 4 × 106 m-1. The main uncertainty arises from limited sampling area in TEM. We estimate 10% relative error in this measurement.\nRevision: We have included the above detail into the supporting information on page 4-6.\nComment 2: Are the properties stable upon thermal cycling? Is there microstructure evolution when the samples are heated to the operating temperature (up to 800 K)? Defect densities and distributions might change when heat is applied. Adding information about that can help strengthen the article (e.g. a figure showing several heating–cooling cycles would help the reader understand whether this is an important effect).\nResponse:\nWe appreciate the constructive point from the reviewer. Heating and cooling cycle measurements were carried out on high performance sample during the revision. An almost negligibly small hysteresis is found, suggesting that the material maintains its thermoelectric performance after heating-cooling cycles (Fig. R12). In addition, we measured XRD for high performance (GeTe) (CuBiS ) sample before and after 0.93 2 0.07 cyclic thermoelectric measurements, as shown in Fig. R13. The sample maintained consistent phase components before and after cyclic thermoelectric measurements. These results demonstrate good thermal stability of the CuBiS alloying sample. 2\nTo investigate microstructure evolution of the optimal sample when the samples are heated to the operating temperature (up to 800 K), we carried out SEM and EDS characterization of the polished surface of the (GeTe) (CuBiS ) sample before 0.93 2 0.07 (Fig. R14a) and after (Fig. R14b) thermoelectric measurements. The results provide compelling evidence that no obvious microstructural changes were observed. Moreover, no noticeable changes in porosity were detected, further validating that the sample did not significantly degrade under high temperatures. Ge, Te, Cu, Bi, and S elements all exhibit uniform distribution in the corresponding EDS mapping before and after thermoelectric measurements. Overall, the microstructural integrity of the synthesized (GeTe) (CuBiS ) material was effectively preserved when the 0.93 2 0.07 samples are heated to the operating temperature.\nTo investigate defect densities and distributions might change when heat is applied, thermogravimetric analysis (TGA) was performed to assess the thermal stability of (GeTe) (CuBiS ) material (Fig. R15). And the results indicated 0.93 2 0.07 negligible weight loss over a wide temperature range, indicating the defect densities and distributions remained largely unchanged.\n(a) (b)\n(GeTe) (CuBiS)\n0.93 20.07\n(c) (d)\nFig. R12. The heating-cooling cycling measurement of the high thermoelectric performance (GeTe) (CuBiS ) sample. (a) Electrical conductivity, (b) Seebeck 0.93 2 0.07 coefficient, (c) Thermal conductivity, (d) ZT.\nFig. R13. XRD patterns of (GeTe) (CuBiS ) sample before and after 0.93 2 0.07 heating-cooling cycling measurement.\nFig. R14. SEM image and corresponding EDS mappings of the surface for the (GeTe) (CuBiS ) sample before (a) and after (b) measurements. The EDS 0.93 2 0.07 mappings for Cu, Ge, Bi, Te, and S are displayed in panels (a1-a5) and (b1-b5), respectively.\nFig. R15. Thermogravimetric analysis for pure GeTe and (GeTe) (CuBiS ) 0.93 2 0.07 sample.\nRevision: We have added related discussion into the revised manuscript.\n\"Moreover, the material maintains its thermoelectric performance after heating-cooling cycles, demonstrating excellent thermal stability (Fig. S13). XRD measurements (Fig. S14) reveal that the sample maintained consistent phase components before and after cycling thermoelectric measurements.\nThermogravimetric analysis (TGA) results (Fig. S15) reveal negligible weight loss after heating, confirming that elemental volatilization is negligible during heating.\nSEM and EDS analysis proves that the sample did not significantly degrade under high temperatures (Fig. S16).\"\nComment 3: In Figure 4e, f, i, and j the authors use HAADF contrast to comment on the distribution of alloying elements and vacancies. Not much can be seen in Figure 4e and f, and based on the distributions shown in Figure 4i and j it is difficult to conclude that Bi, Cu, and S substitute preferentially on specific lattice sites or to localize individual vacancies. I suggest softening these statements or supporting them with additional evidence (for example EDS/EELS mapping or simulations).\nResponse:\nThank you for your thoughtful comments. We agree that directly and unambiguously determining the exact lattice sites of specific elements (Bi, Cu, S) or individual vacancies based solely on the Z-contrast (atomic number contrast) images in Fig. 4e, f, i, j is indeed challenging.\nIn response to your suggestion, we have revised the corresponding statements in the manuscript on page 9. Specifically, the phrase \"suggesting that heavily doped Bi atoms and lighter Cu atoms preferentially substitute into the Ge sites\" has been modified to state: \"the Z-contrast intensity of the Ge atomic columns exhibits significant local variations (inhomogeneity), indicating pronounced compositional fluctuations at the microscopic scale. Such local compositional fluctuations serve as a key microstructural mechanism for introducing mass-field perturbations and enhancing phonon scattering.\"\nFurthermore, to strengthen the logical basis of this revised interpretation, we have added an explanation of the HAADF imaging principle—where intensity is approximately proportional to Z²—before the analysis. This logically links the observed inhomogeneity in Ge column contrast to \"compositional fluctuations\" (which may arise from Ge vacancies and substitution by atoms of different Z). These modifications directly address the core concern: replacing an earlier, potentially overinterpreted conclusion with a more accurate and defensible description of microstructural features (compositional inhomogeneity), while providing the necessary rationale through the Z² dependence to make the argument more rigorous without exceeding the support of the evidence.\nWe believe these revisions have appropriately softened the conclusions, better aligned the discussion with the evidence, and enhanced the clarity and rigor of the presentation. Thank you again for this valuable suggestion.\nRevision: We have revised the corresponding statements in the manuscript on page 9.\n\"The intensity in the HAADF-STEM image is approximately proportional to the atomic number Z2.\"\n\"the Z-contrast intensity of the Ge atomic columns exhibits significant local variations (inhomogeneity), indicating pronounced compositional fluctuations at the microscopic scale. Such local compositional fluctuations serve as a key microstructural mechanism for introducing mass-field perturbations and enhancing phonon scattering.\"\nComment 4:\nIs the methodology sound?\nThe overall methodology appears sound, but some important experimental details are missing and should be provided to ensure reproducibility:\nFor SEM: specify detector type (SE or BSE), acceleration voltage, probe current (or beam conditions), and working distance.\nFor STEM: specify acceleration voltage, convergence semi-angle, collection angles for the HAADF and BF/ADF detectors, and the approximate probe size. Please also describe how the STEM samples were prepared (FIB, ion milling conditions, etc.).\nResponse:\nThank you for your comments.\nDetailed SEM Parameters: The microstructure and composition analysis were performed using a FEI Quanta 250 FEG scanning electron microscope equipped with an EDS detector (Inca, Oxford instruments). Micrographs were acquired primarily using the Secondary Electron Detector (SED) at an acceleration voltage of 20 kV, a beam condition set to a spot size of 3.0, and a working distance of 10 mm to optimize both image contrast and EDS signal.\nDetailed STEM Parameters: The characterization was performed using JEOL JEM-ARM300F2 aberration-corrected scanning transmission electron microscope (STEM) operated at an acceleration voltage of 300 kV. The STEM imaging was conducted with a probe size of approximately 8c, a convergence semi-angle of about 25 mrad, and collection angles ranging from 90 to 370 mrad. Samples for STEM observation were prepared by mechanical grinding followed by ion milling. The ion milling process was carried out using Ar⁺ ions with the specimen mounted on a liquid nitrogen-cooled stage to minimize beam-induced damage. The thinning procedure consisted of two stages: an initial coarse thinning at a higher voltage (4-5 kV), followed by a final precision polishing at a lower voltage (1-2 kV) to obtain an electron-transparent area free of amorphous surface contamination, suitable for high-resolution imaging.\nRevision: Experimental details were provided in revised manuscript on Page 21.\n\"The scanning electron microscopy (SEM) (FEI Quanta 250 FEG) equipped with the energy dispersive spectrometry (EDS) (Inca, Oxford instruments) was performed on the microstructure investigation of the samples. Micrographs were acquired primarily using the Secondary Electron Detector (SED) at an acceleration voltage of 20 kV, a beam condition set to a spot size of 3.0, and a working distance of 10 mm to optimize both image contrast and EDS signal.\"\n\"JEOL JEM-ARM300F2 aberration-corrected scanning transmission electron microscope (STEM) operated at an acceleration voltage of 300 kV. The STEM imaging was conducted with a probe size of approximately 8c, a convergence semi-angle of about 25 mrad, and collection angles ranging from 90 to 370 mrad. Samples for STEM observation were prepared by mechanical grinding followed by ion milling (GATAN 691). The thinning procedure consisted of two stages: an initial coarse thinning at a higher voltage (4-5 kV), followed by a final precision polishing at a lower voltage (1-2 kV) to obtain an electron-transparent area free.\"\nComment 5: EDS is mentioned in both SEM and STEM, but no EDS data are shown. Either include representative EDS results or clarify how EDS was used and why the data are not shown.\nResponse:\nWe are sorry that we made a type error. We only use EDS in SEM measurements. We have provided the SEM-EDS mapping results in the revised supporting information (Fig. S16).\nComment 6: Small comments Line 50: duplicated “potential”.\nResponse: Thanks for your comment. The duplicated “potential” has been deleted.\nComment 7: Line 80: “secondary phases”.\nResponse:\nThanks for your comment. We have corrected the mistake.\nComment 8: Line 106: I suggest adding a brief comparison of the obtained average zT values with state-of-the-art GeTe-based thermoelectrics.\nResponse:\nThanks for your suggestions. We compare average ZT values with state-of-the-art GeTe-based thermoelectrics in Fig. R10b (Fig. 7b in the main text).\nComment 9: Line 163: “magnified” instead of “further amplified”.\nResponse:\nThanks for your comment. We have modified the words.\nComment 10: Line 171 and 180: Figure 3 is referenced incorrectly.\nResponse:\nThanks for your comment. We have corrected this error.\nComment 11: Line 190: likely also references a wrong figure, please check.\nResponse:\nThanks for your comment. We have corrected this error.\nComment 12: Line 218: Figure 3 is introduced after Figure 4; consider reordering or adjusting the text.\nResponse:\nThank you for comment. In original manuscript, we first discussed the variation trend of thermal conductivity in Fig. 3a and 3b. Then, we explained the origin of the reduction in lattice thermal conductivity according to TEM characterization results from Fig. 4. We further elucidate the underlying mechanism responsible for the decrease in lattice thermal conductivity by Debye-Callaway model calculations in Fig. 3c and 3d.\nWe hope that the revised manuscript is now suitable for publication in Nature Communications. Thank you for your time and consideration.\nSincerely and best regards\nYours sincerely\nGuodong Tang\nOn behalf of all co-authors"}, {"round": 2, "reviewer_comments": {"reviewer_1": "Authors have addressed the raised issues and considerations.\nThe manuscript is recommended for acceptance.", "reviewer_2": "Thank you for your careful revisions. The authors have addressed the requested changes, and the manuscript has improved accordingly. One minor point: I suggest tempering the statement that negligible TGA mass loss implies unchanged defect densities, since TGA mainly indicates mass stability. With this small clarification, I recommend publication."}, "author_response": "We appreciate the positive comments from the reviewer. We corrected the discussion of last Response letter during this revision. The manuscript discussion is consistent with this claim.\n\"To investigate the mass stability when heat is applied, thermogravimetric analysis (TGA) was performed to assess the thermal stability of (GeTe) (CuBiS ) material 0.93 2 0.07 (Fig. R1). And the results indicated negligible weight loss over a wide temperature range, confirming that elemental volatilization is negligible during heating.\"\nFig. R1. Thermogravimetric analysis for pure GeTe and (GeTe) (CuBiS ) 0.93 2 0.07 sample.\nWe hope that the revised manuscript meets the standards for publication in Nature Communications. Thanks for your time and consideration.\nWith kind regards,\nGuodong Tang\nNanjing University of Science and Technology,\nNanjing 210094, China.\nE-mail: tangguodong@njust.edu.cn\nFax: +86-25-84315159; Tel: +86-25-84315159"}]

Decision letter