Optically-controlled phonon-specific phase transitions from graphite to diamond

Domain: physics
Published: 2025-12-09
Editorial outcome: major_revision

Abstract
Controlling phase transition processes and the atomic structure of new states with light has emerged as a highly challenging frontier in condensed matter physics and material science. The conversion of graphite to diamond typically relies on high-pressure and high-temperature conditions, while the advent of ultrafast laser has opened entirely new possibilities for dynamically controlling such structural transformation under non-thermodynamic state. Herein, employing state-of-the-art first-principles non-adiabatic molecular dynamics simulations, we elucidate ultrafast pathways of light-induced graphite-to-diamond phase transition and reveal the laws governing the selective formation of cubic or hexagonal diamond, as well as their subsequent structural evolution, by regulating laser parameters. Such optically controlled diamond formation stems from early-stage structural reconstruction driven by electron-phonon couplings and indirect excitation of specific phonon modes (e.g. B2 3g modes) via phonon-phonon couplings. The competition between newly generated phonons from indirect excitation constitutes the key factor determining the fine structure of final product. This work not only demonstrates effective modulation of structural phase transition through photoinduced non-thermal pathways, but also provides important strategy for efficient and eco-friendly material synthesis via optical control.

Introduction
The conversion dynamics of graphite-to-diamond and their underlying mechanisms have been the subject of extensive research1–7. Such phase transitions between carbon allotropes involve alterations in the bonding pattern of carbon atoms. To achieve precise control over material structures and thereby synthesize new carbon materials with unique properties, it is crucial to understand the intrinsic driving forces behind structural evolution and the means of reaction regulation. High pressure can effectively reduce the free energy barrier of phase transitions8, therefore, earlier studies have mainly focused on converting graphite into diamond under high pressure9–13, followed by research utilizing of shock waves14–19. Over half a century ago, Bundy et al. reported the successful synthesis of man-made cubic diamond (CD)9 and hexagonal diamond (HD)13 under high-pressure, high-temperature (HPHT) conditions, with synthesis temperatures exceeding 2000°C and 1000°C, respectively. Recently, the breakthrough in successfully synthesizing nano-sized, high-purity HD from graphite under HPHT conditions has further advanced the research progress in engineering the desirable features of carbon allotropes3,20. In 1961, shock-induced graphite-to-diamond phase transitions were also reported in ref. 14. The microscopic mechanisms underlying graphite-to-diamond phase transition under pressure1,3,21–23 and shock waves2,24,25 remain a focus of research to this day. For instance, Armstrong et al. observed the phase transition process in shock compressed graphite on picosecond timescale using X-ray diffraction, and found that the formation of HD is kinetically more favorable than that of CD under rapid compression19; while Chen et al., from the perspective of computational research, further clarified that different interlayer sliding distances may lead to different products during shock-induced phase transitions2.

Following the successive experimental and theoretical reports on the induction of graphite-to-diamond transition via hole doping of the valence bands at room temperature26,27, experimental and theoretical explorations into photoinduced graphite-to-diamond phase transition have been initiated. Raman et al. clearly captured the process of photoinduced interlayer compression leading to bond formation using electron diffraction techniques28. Carbone et al. detected signals of interlayer bond formation around ~180 fs after photoexcitation via fs-resolved electron energy loss spectroscopy29. Nüske et al. observed the formation of nanoscale cubic diamond crystals in the laser-irradiated highly oriented pyrolytic graphite (HOPG) sample using Raman spectroscopy and X-ray diffraction7. Duan et al. observed ultrafast formation of a transient two-dimensional diamond-like structure under femtosecond laser irradiation using MeV ultrafast electron diffraction30. Furthermore, several STM-based studies have identified the regions of laser-excited sp3-bonded domain formation involving interlayer sliding, intralayer buckling, and periodic interlayer bonding31,32. Meanwhile, computational studies on the formation mechanism of photoinduced interlayer bonding in graphite have been emerging30,33–35. Luo et al. emphasized the significance of the stacking mode in influencing the bonding patterns between adjacent graphite layers and the formation of different final structures30. Song et al. demonstrated a non-adiabatic dynamic process of forming sp3-hybridized carbon structures within a few hundred femtoseconds after laser irradiation and highlighted the importance of electron–phonon coupling in such processes34. However, there remains a substantial gap in unraveling the reaction pathways and the key mechanisms of light-induced graphite-to-diamond phase transition under nonequilibrium regimes on ultrafast timescales, and the microscopic dynamic picture of such phenomena continues to be a fascinating challenge.

Given the current lack of a comprehensive reaction pathway of light-induced graphite-to-diamond conversion and an understanding of the intrinsic mechanisms of such reactions on ultrafast timescales, we herein report the nonequilibrium reaction dynamics of photogenerated charge carriers and lattice motions in such transitions, as well as how the excitation modes are correlated to the ultimately formed diamond atomic structures. Through state-of-the-art first-principles non-adiabatic excited-state dynamics simulations, we reveal the complete reaction pathway diagram of light-driven graphite-to-diamond phase transitions, as illustrated in Fig. 1. The phase transition pathway and final structure are closely correlated with the proportion of photoexcited electrons. Excessive excitation leads to the formation of an amorphous state, while insufficient excitation fails to drive the graphite structure to overcome the reaction energy barrier and complete the phase transition. An appropriate amount of electron excitation is crucial for the formation of the diamond structure. Our results demonstrate the rational control of the phase transition process and products by optical means. Under the action of the laser field, electron–phonon coupling induces specific phonon displacements, thereby giving rise to different degrees of interlayer sliding and bonding modes. In particular, the strong excitation of B2 3g and TO-5 phonon modes guides the selective formation of cubic and hexagonal diamonds, respectively. We find that the final fine carbon structure of the phase transition is strongly correlated with the degree of excitation and propose a light wavelength-fluence phase diagram for photoinduced diamond generation, which reveals the optical regulation capability of ultrafast lasers with appropriate light field conditions on the phase transition process. Our results highlight the subtle nonequilibrium reaction pathways and intrinsic dynamic mechanism of laser-induced graphite-to-diamond phase transition, providing new insights and directions for achieving precise optical control of the atomic structure of materials.

Results
Nonequilibrium pathways of light-induced graphite-to-diamond phase transition
We first apply a Gaussian-shaped laser pulse with a photon energy of 1.55 eV and a maximum field strength of E0 = 0.514 V/Å on the AB stacked graphite crystal. The laser pulse is polarized along the armchair direction of graphite with a fluence of 120.5 mJ/cm2, which is below the previously reported optical damage thresholds of 130–250 mJ/cm2 for graphite28,36–38. The nonequilibrium reaction pathway of light-induced transition from graphite to diamond is reported in Fig. 2, where the characteristic atomic structures and the corresponding energy changes during the reaction are displayed in Fig. 2a. Atomic structures in the insets are extracted directly from the trajectory of non-adiabatic molecular dynamic simulations, representing the structure characteristic of different stages of the phase transition: (i) initial graphite structure, (ii) interlayer contraction after excitation, (iii) intralayer buckling, (iv) formation of sp3 bonds, (v) generation of diamond-like structure, and (vi) the final structure of phase transition, respectively. The calculated single-point energy of corresponding structures indicates that a potential energy barrier of ~1.0 eV/atom needs to be overcome for such photoinduced phase transition reaction. Upon photoexcitation, the electronic structure significantly changes from ~100 fs (see Suppl. Fig. 1) and opens an energy band gap of ~3.27 eV at 250 fs, which represents the electronic signature of the formed sp3-hybridized carbon network.

To further trace the structural relaxation process and identify the stable final products of the phase transition, we apply a thermal bath to anneal the photoexcited system down to room temperature at an annealing rate of 300 K/ps, as shown in the Suppl. Fig. 2. The annealing process starts from the state obtained at 400 fs in the non-adiabatic simulation and continues up to 8.0 ps after the temperature reaches ~300 K. Such annealing process addresses, to some extent, the issue of insufficient energy dissipation in non-adiabatic excited-state simulations and provides an approach to access the ultimate stable structure after photoexcitation relaxation, since the evolution of lattice structures typically takes at least a few picoseconds to complete39,40. Meanwhile, the annealing relaxation process also mimics the diffusion and dissipation of energy from the local lattice structure to the surrounding regions in practical scenarios. As shown in Fig. 2a, through the annealing relaxation, the metastable sp3-hybridized carbon lattice further evolves into a stable CD crystal structure, exhibiting a band gap that is further widened to 3.63 eV, and its electronic band structure can be directly compared with that of perfect CD.

To obtain the microscopic dynamics information of sp2-to-sp3 phase transition, the time variation of three structural parameters, namely, graphite interlayer distance Δd, the intralayer buckling height Δz and tetrahedral order parameter qt, are presented in Fig. 2b. The tetrahedral order parameter qt is defined as41
qt = 1 - 3/8 * sum_{i=1}^{3} sum_{j=i+1}^{4} (cos theta_{ikj} + 1/3)^2 (1)
where theta_{ikj} is the angle formed by the k-th atom and its nearest neighbors i and j. The qt accurately characterizes the structural similarity of the intermediate state generated during photoexcited sp2-to-sp3 phase transition with that of perfect diamond. For a perfect tetrahedral configuration at 0 K, cos theta_{ikj} is equal to -1/3, yielding qt = 1 for diamond, as illustrated in Fig. 2b.

Upon light irradiation, the graphite layer spacing Δd undergoes a rapid compression from 3.4 Å to ~2.3 Å within 160 fs. A pronounced sp2-to-sp3 structure transformation initiates at around 160 fs. Such ultrafast interlayer compression and sliding processes in graphite under light irradiation have been widely observed in previous experiments7,28,30–32, and the timescale for the initial formation of sp³ bonds is also consistent with the ~180 fs reported in previous experiments29. From then on, the interlayer distance Δd further reduces to ~1.9 Å, while the buckling height Δz, which characterizes the degree of out-of-plane distortion, rapidly increases to more than 0.3 Å. Such structural changes in graphite provide the necessary spatial conditions for the formation of interlayer sp3 bonds. According to the criterion that a chemical bond forms once the distance between two carbon atoms in adjacent layers is less than 1.8 Å, interlayer C-C bonds start to form rapidly from 160 fs onwards, with the average number of interlayer bonds NIB reaching ~4 at ~250 fs (Suppl. Fig. 3). The analysis of time-dependent electron localization function and differential charge density, as shown in Suppl. Figs. 4, 5, provide further electronic evidence for the formation of sp3 bonds. The time evolution of the tetrahedral order parameter qt, shown in Fig. 2b, suggests that graphite evolves into a diamond-like structure very close to the diamond configuration within ~250 fs after photoexcitation. Until 400 fs, Δd remains below 2.0 Å, NIB stabilizes at 4 with minimal fluctuations, and qt varies around 0.95, all of which imply that the light-induced diamond-like structure enters a structural metastable state. During the subsequent annealing process, the interlayer spacing Δd, buckling height Δz and the number of interlayer bonds NIB stabilize at ~2.0, ~0.35 Å and 4, respectively. In contrast, the tetrahedral order parameter qt rises from ~0.95 to 1, which clearly indicates that the metastable diamond-like structure relaxes into a perfect CD structure and acquires an electronic band structure very similar to that of CD. To verify the influence of initial state selection on the annealing processes, we extract another configuration from the rt-TDDFT trajectory at 280 fs as the initial state for the thermal relaxation process, as shown in the Suppl. Fig. 6. A comparison of Fig. 2b and Suppl. Fig. 6 reveals that although the relaxation processes initiated from different excited-state configurations exhibit subtle differences in specific dynamic behaviors, the final phase transition structure remains unaffected.

Given the features of the atomic and electronic structure evolution, we propose the laser-induced phase transition from graphite to diamond undergoes three distinct key stages: (i) structure distortion of graphite; (ii) sp2-to-sp3 bonding transition; (iii) relaxation into the ultimate phase, delineated by the different background colors in Fig. 2. It is worth mentioning that under the same laser excitation condition, AA stacked graphite undergoes a similar phase transition to AB stacked graphite (Suppl. Fig. 7).

Ultrafast dynamics of excited charge carriers
Based on the non-thermal reaction pathways of graphite-to-diamond conversion identified above, we next focus on elaborating the nonequilibrium dynamics of photogenerated charge carriers within the femtosecond timescale, which is crucial for initiating the phase transition. In Fig. 3a, we track the changes of electronic structures and photogenerated carrier distribution along the light-induced carbon structure conversion and present the corresponding electronic states at each of the three stages. The blue and red dots represent the photogenerated electrons and holes, respectively, and the size of the dots depict the population of excited charge carriers. Under the ultrafast laser pulse with a photon energy of 1.55 eV and a fluence of 120 mJ/cm2, the electron subsystem of graphite is boosted immediately in the vicinity of a high symmetry point, with both resonance excitation and multiphoton absorption observed. The percentage of excited electrons reaches a maximum of about 3.8% during the direct action of laser light (see Suppl. Fig. 8). By the end of the first stage of phase transition at 160 fs, the electrons excited from the π band to the π* band have scattered into the unoccupied σ interlayer band, as shown in Fig. 3b. Such redistribution of photogenerated electrons accounts for the weakening of in-plane C-C bonds, resulting in the lattice instability of graphite and promoting the out-of-plane distortion.

We further carry out a thorough analysis of the carrier occupancy in each electronic state during the light-induced process. Temporal evolution of the distribution of the photogenerated charge carriers (Δq) in each orbital is presented in Fig. 3c. We find that starting from ~100 fs after the end of light irradiation, a small fraction of photoexcited electrons is scattered to high-energy orbitals, as indicated by the orange arrow in Fig. 3c. The new distribution is the result of Auger recombination (AR), in which the excess energy released by electron-hole recombination scatters electrons to higher energy levels. On the other hand, in the second stage of phase transition (>160 fs), an increase of charge carriers is also observed near the Fermi level, highlighted by the green dashed line in Fig. 3c. It may be attributed to the energy release from high-energy electron collisions to create new electron-hole pairs, namely impact ionization (II), leading to an increase in charge carrier occupancy near the band edges. It is worth noting that although the Hamiltonian used in our non-adiabatic calculations does not explicitly include electron-electron scattering terms42, the incorporation of multiple k-points and the presence of lattice distortions (or virtual phonons) allow electron scattering to be included to a certain extent. This enables us to capture the key Auger process and carrier transport. Since adiabatic TDDFT tends to underestimate the carrier-carrier interaction and the scattering rates in real systems to some extent, the actual electron-electron scattering effects might be more pronounced than what the current simulation results show.

Specifically, during the first stage of phase transition (<160 fs), photoexcitation occurs mainly between the three highest occupied orbitals and the three lowest unoccupied orbitals, that is, from valance band VB1-3 (counted in the order of decreasing energy from the Fermi level) to conduction band CB1-3 (counted in the order of increasing energy from the Fermi level), as shown by the blue and red curves in Fig. 3c. A small amount of excited charge occupation is also observed in CB5 and CB6 during this stage. In the second stage of phase transition where interlayer sp3 bonds form, the charge carrier occupancy of VB2, VB1, CB1, CB2 increase significantly, while more electrons are scattered into high-energy orbitals, such as CB6 and CB7. Upon entering the relaxation stage at ~250 fs, ~2% of the photogenerated charge carriers are retained. The redistribution of photogenerated charge carriers is the result of the combined action of AR and II processes. Among them, AR is the dominant process that further scatters excited electrons into higher energy levels, thereby reducing the in-plane stability of graphite and promoting the formation of interlayer bonds.

Key role of specific phonon excitations
Based on the understanding of the electronic origin of the phase transition, we further investigate the lattice dynamics induced by the redistribution of photogenerated charge carriers through electron–phonon coupling, as well as the influence of excited phonon modes on the optical pathway of graphite-to-diamond conversion. Under light irradiation, the electronic subsystem of graphite is rapidly excited within tens of femtosecond, as shown in Fig. 3. To identify and track the emergence and evolution of excited phonons, we project the real-time displacement of carbon atoms onto the 48 phonon eigenvectors of the initial graphite structure. The projected intensity, shown in Fig. 4a, can be expressed as d_i * u_{ij}, where d_i is the displacement vector of the i-th atom from the ground state at t=0, and u_{ij} is the phonon eigenvector of the j-th phonon branch.

We find that three phonon modes, i.e., B1g, Ag and B3g modes, are gradually excited during the first stage of the phase transition, as demonstrated in Fig. 4b. The excited interlayer shearing modes B1g and Ag are responsible for the occurrence of interlayer sliding in graphite, which is the result of π-π* optical transition43. Another excited mode, B3g, accounts for the interlayer compression of graphite. The excitation and cooperation of these specific phonon modes provide the necessary conditions for the initiation of the graphite-to-diamond phase transition. More intriguingly, starting from ~160 fs, a fourth phonon mode, namely B2 3g, is gradually excited through phonon–phonon coupling, as indicated by the red triangles in Fig. 4a. This mode represents the out-of-plane non-resonant motions of carbon atoms that lead to the intralayer buckling of graphite. To further explicitly demonstrate the phonon–phonon coupling effects during the phase transition, we calculate the potential energy surfaces (PES) of B2 3g mode under the condition where the B3g mode exhibits different displacements. The results shown in the Suppl. Fig. 9 indicate that the intense excitation of B3g mode can effectively induce substantial changes in the PES of the B2 3g mode. The average atomic displacement |Δr| of the above four primarily excited phonon modes at Γ point is also calculated and presented in Suppl. Fig. 10, to further demonstrate the lattice dynamics and anharmonicity during the excitation and phase transition process in real space. Similar behaviors to those observed in the phonon projection plot have been observed, see Suppl. Fig. 10.

Since the interlayer spacing of the excited graphite system remains within 2 Å after 160 fs, adjacent layers begin to form interlayer sp3 bonds through deformation, and metastable diamond-like structure appears at ~250 fs. In the light-induced formation of the CD structure, other transverse optical (TO) phonons are also induced to experience weak excitation from the second stage onwards. Similar coupling behaviors of multiple excited phonons have also been observed in other systems44–47, for example, the coupling between in-plane and out-of-plane polarizations in ferroelectric material α-In2Se3 47.

The formation of different carbon allotropes (sp3-bonded) from graphite is an issue of great interest. Our independent non-adiabatic excited-state dynamic trajectories obtained under different photoexcitation conditions suggest that CD, HD, and orthorhombic W-carbon with 5- and 7-membered rings could all be the outcomes of optically driven phase transitions in graphite. By comparing the types and intensities of excited phonons that result in different final carbon structures, we conclude that the excitation of the B1g, Ag and B3g modes is a prerequisite for initiating the deformation of graphite structure and providing the essential lattice distortion for the formation of sp3 bonds. Although we only observed the formation of the W-carbon under the laser conditions employed, different carbon allotropes48–50 may also form when specific phonon modes are excited through the combined effects of electron–phonon coupling and phonon–phonon interactions.

There is a strong correlation between the structure of light-induced phase transition products and the four most strongly excited phonon modes. Figure 4c displays the average amplitudes of different excited phonons during the period of 300 to 400 fs, corresponding to the dynamic trajectories that lead to the formation of different final structures. By analyzing the excitation strengths of all six phonon modes selectively excited from the second stage of the phase transition, including B2 3g and five TO modes (also see Suppl. Fig. 11), we find that, compared to the other modes, the strongest excitations of B2 3g, TO-5 and TO-4 modes dominate the generation of the CD, HD and W-carbon structure, respectively. As illustrated in Fig. 4d, the dependence of the light-driven product on the excitation phonons is the result of the competition between the excited phonon modes in the second stage of the phase transition after photoexcitation. The intrinsic vibrational modes of the most prominent phonons, coupled with the sliding and compression phonons excited in the first stage, determine the upper and lower alignments of the in-plane buckling and thus the final atomic structure of the phase transition product.

Optical regulation of phase transition
After addressing the driving forces and microscopic mechanism of light-induced graphite-to-diamond phase transition, we next explore how particular laser conditions affect the conversion of graphite to diamond. To distinguish the atomic structure of CD and HD, we further define a bond parameter Q, expressed as
Q = 1/3 * sum_{i=1}^{4} (cos min |γ_{imnj}| - 1/2)^2, j=1,2,3 (2)
where m and n represent the two carbon atoms of a specific C-C bond, and i and j are the other three nearest neighboring carbon atoms of m and n, respectively. For each atom i, the dihedral angle γ_{imnj} determined by the four atoms (i, m, n and j), has three possible values corresponding to three different j. The minimum values of |γ_{imnj}| are 0° and 60° for standard overlapping or crossed carbon-carbon bonds, respectively. This means that the Q_{mn} value of a standard eclipsed C-C bond is 0, while that of a crossed C-C bond is 1, as illustrated in Suppl. Fig. 12. Therefore, the average Q value of all C-C bonds in CD and HD is close to 1 and 0.75, respectively. To clarify, the bond parameter Q is used to distinguish CD and HD structures, while the tetrahedral order parameter qt characterizes the tetrahedral configuration in carbon structures.

In Fig. 5, we report that, at a pump wavelength of 800 nm (1.55 eV), the structures obtained from the light-driven phase transition exhibit a significant dependence on the laser fluence. The dashed lines indicate the approximate boundaries between the different carbon structures. The diagram suggests that CD is the main product of light-induced phase transition at laser fluences of ~120–130 mJ/cm2, while graphite transforms into hexagonal diamond (HD) and W-type carbon when the fluence is above and below this range. In the case of fluence value below ~90 mJ/cm2, the system lacks sufficient excitation energy to initiate the first stage of the phase transition. In contrast, when the laser power is excessively high, it results in the inability to properly excite the required phonon modes during the second stage of the reaction, and thus the crystalline structure fails to form.

We propose the wavelength-fluence phase diagram of the graphite-to-diamond transition in Fig. 5b, where the laser wavelength ranging from 600 to 1000 nm and the light fluence reaching the order of magnitude of 10² mJ/cm² are all experimentally achievable36,51–53. Based on the thirty independent non-adiabatic photo-reaction trajectories, we find that the light-driven diamond conversion of graphite is mainly achieved in the region close to the graphite damage threshold and requires sufficient and appropriate laser power. The longer the wavelength, the lower the required laser power (also see Suppl. Fig. 13). It can also be observed that within the fluence range where diamond structures are formed, the CD structure is more likely to be generated in the middle interval, while the HD structure is more prone to form in the upper and lower regimes. Laser fluence is directly related to the amount of electronic excitation and the specific modes of phonon excitation. Over-excitation leads to system collapse, while insufficient excitation fails to drive the graphite structure to overcome the reaction barrier and complete the phase transition. As indicated in the Suppl. Fig. 13, the electronic excitation level in the phase transitions that result in the formation of the CD or HD ranges from ~3.4% to 4.2%.

To gain further insight into the light-induced graphite-to-diamond phase transition mechanism revealed above, we compare the dynamic behavior of photoinduced structural transformation in graphite across different supercell sizes within the rt-TDDFT non-adiabatic computational framework, and the results show that the phase transition mechanism is essentially consistent (Suppl. Fig. 14). Compared to large supercells or experimental scenarios, the direct interaction of laser pulses with the interior of small supercells is likely to trigger a faster and more sensitive response in phase transitions simulations. Furthermore, investigations into the effects of laser polarization direction (Suppl. Fig. 15) and graphite defects indicate that laser irradiation with polarization perpendicular to the graphite plane barely generates sufficient excited electrons to induce phase transitions, while defects would also hinder the order-to-order phase transition process. These results imply that in the case of polycrystalline graphite, the existence of grain boundaries and high defect concentrations may substantially reduce the efficiency of the photoinduced graphite-to-diamond phase transition.

Methods
First-principles excited-state molecular dynamics simulations
First-principles non-adiabatic molecular dynamics simulations were performed using time-dependent ab initio package (TDAP)58,59, where the electron dynamics are captured within the framework of real-time time-dependent density functional theory (rt-TDDFT) and the coupled motion of electrons and nuclei is described by Ehrenfest dynamics60. Graphite crystal is simulated with a 2×3×1 supercell, containing two AB stacked sublayers of 16 carbon atoms. The initial lattice dimensions of the supercell are 4.92, 4.26, and 6.80 Å, respectively, and the graphite interlayer distance is 3.40 Å. Numerical atomic orbital basis set with double zeta polarization (DZP) and Troullier-Martins pseudopotentials are adopted. We employ the local density approximation (LDA)61 to describe the electronic exchange-correlation energy. An auxiliary real-space grid equivalent to a plane-wave cutoff of 150 Ry is used, and the Brillouin zone is sampled by a 4×4×3 k-mesh. Linearly polarized laser pulse is applied along the armchair direction (y-axis) of graphite, with a Gaussian-enveloped waveform E=E0 cos(ωt)exp[-t^2/2σ^2], where the photon energy ℏω is 1.55 eV, field intensity E0 = 0.514 V/Å at time t=48 fs. The timestep of 0.04 fs is applied for both electron and ion motions, evolving in a constant pressure-energy (NPE) ensemble, where pressure is controlled by the Parrinello-Rahman method62. After the light field irradiation, the total energy of the system remains essentially constant, with only a slight drifting of ~0.0002 eV/fs per atom caused by the accumulation of numerical errors.

Band structure and phonon calculations
Band structures are calculated via Vienna Ab Initio Simulation Package (VASP)63 adopting the projector augmented wave (PAW) method. Phonon frequency and eigenvectors are calculated within density functional perturbation theory (DFPT) using PHONPY64.

Born–Oppenheimer molecular simulation and structural relaxation
The structure relaxation from metastable light-induced product configuration is performed with CP2K package65. Initial atomic structure, velocities and temperature for the annealing simulation is obtained from the configuration of the non-adiabatic rt-TDDFT simulation at 400 fs. All configurations are annealed to room temperature by an 8 ps constant-pressure Born-Oppenheimer MD simulation with a cooling rate of 300 K/ps and a timestep of 0.1 fs, to achieve the state of stable carbons structure. Valence electron wavefunctions are expanded in a single zeta Gaussian basis set (SZV)66. Goedecker-Teter-Hutter (GTH) pseudopotentials67 and BLYP exchange-correlation functional68,69 are used.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This paper presents a computational study of the laser-driven structural transition of graphite to diamond. The authors use RT-TDDFT together with molecular dynamics to simulate the coupled electron-nuclear dynamics triggered by 50-fs laser pulses, and find that, if the laser fluence is sufficiently high (but not too high), graphite converts to the cubic or hexagonal diamond phase. About 30 trajectories are calculated, and a detailed analysis is provided in terms of the evolution of the band structure, the excited-state population, and the population and significance of various phononic states. From this, the authors conclude that there are realistic and achievable pathways towards purely optically controlled graphite-diamond transitions.\n\nThe topic of graphite-to-diamond phase transitions is an old and well-studied one, with an emphasis on high pressure and shock waves. Structural transformations via laser excitation are also a well-studied area in materials science. To my knowledge, a detailed theoretical study which explores concrete optical pathways for graphite-to-diamond seems indeed novel, and could be of significant interest in the sense of stimulating experimental research.\n\nWhile I recognize that this is potentially interesting work, there are in my opinion significant problems with the analysis and interpretation of the results which prevent me from recommending publication.\n\n1. The authors propose that the excited-state population distribution is dominated by two effects: Auger recombination and impact ionization. Auger recombination is an effect where electron-hole recombination energy gets transferred via Coulomb interactions to a third carrier, exciting it to a higher energy state. The ALDA does not capture Auger recombination since it is a many-body effect beyond the local approximation. Auger rates are typically obtained using Fermi’s Golden Rule in the quasi-static case. However, Zhou, Lu and Prezhdo, Nano Lett. 21, 756 (2021) have shown that the Auger effect can also be incorporated into RT-TDDFT coupled with MD, but one needs to explicitly include Coulomb scattering matrix elements into the Hamiltonian. Therefore, based on ALDA-TDDFT results alone it is not possible to conclude that Auger recombination is responsible for the population of excited states shown in the instantaneous band structures in Fig. 3.\n\n2. In that context, have the authors checked whether the total energy (electrons plus nuclei) is conserved (at least up to 400 fs, before the dissipation sets in)?\n\n3. Also, the LDA gap of diamond is about 4.3 eV. The authors state that at 250 fs the gap is about 3.27 eV. Does the gap open up further after that?\n\n4. Figure S4 shows the differential charge density, which is used by the authors to identify the formation of new bonds during the time evolution. A much better indicator of bond formation is the time-dependent electron localization functon(TDELF). Have the authors considered this quantity?\n\n5. The authors then discuss the role of specific phonon excitations in the structural phase transition process. The phonons considered are those of the initial graphite structure. As the laser pulse hits the graphite, several of these phonon modes are excited. Figure 4 then shows how the projected intensity of the phonon modes grows over time, well into the second stage of the evolution (>160 fs). It is then discussed how the various phonon modes contribute to the structural change. In my opinion, this analysis is only meaningful in the early stages of the laser excitation, perhaps up until 50 fs or so. After that, the structure of the system has changed so significantly that it makes no sense to project onto the graphite phonon eigenvectors, since the harmonic approximation would no longer be valid. In other words, it is fine to say that the laser triggers phonon modes corresponding to sliding and buckling motion, but once that motion goes towards a new structural phase, the phonon picture based on the initial phase is no longer meaningful. To see this, the projected phonon intensities in Fig. 4a should be expressed as amplitudes in units of the lattice constant or bond length, which would then show when the anharmonic regime would be reached.\n\n6. Also, the authors mention phonon-phonon coupling, but no explicit illustration or analysis is given.\n\n7. In the methods section, it is discussed how the time propagation up until 400 fs is done with the TDAP code using ALDA, and after 400 fs the CP2K package is used to do BO molecular dynamics based on the configuration and temperature at 400 fs, and using the BLYP functional. How can the authors be sure that these two methods match? Looking at Fig. 2b: the middle panel shows the buckling height Delta z, which is seen to decrease between 0.3 and 0.4 ps, but when the MD kicks in at 0.4 ps, Delta z suddenly increases. A similar behavior, although less pronounced, is seen in the other two panels of Fig. 2b. Are these artifacts of the computation? How much can the final relaxed state be trusted?\n\n8. Lastly: the calculations are done using a 16-atom supercell. I can imagine that the computational effort that went into this paper was quite substantial. Nevertheless, this supercell seems quite small, given the massive structural changes that are being simulated here, where the system surely goes through various stages of disorder before reaching again an ordered phase. How can one be sure that the supercell size is adequate to capture this?", "reviewer_2": "This manuscript presents a compelling computational study of ultrafast, laser-induced phase transitions from graphite to diamond, utilizing state-of-the-art non-adiabatic molecular dynamics (NAMD) simulations. The authors propose that light-driven, phonon-specific mechanisms govern the selective formation of either cubic or hexagonal diamond under non-equilibrium conditions. The work is timely and relevant to the fields of laser-matter interaction, phase transformation, and sustainable materials synthesis, with potential implications for energy-efficient diamond production.\n\nThe manuscript is generally well-written, and the simulations appear to be thoughtfully designed. However, several points require further clarification and discussion before the manuscript can be recommended for publication.\n\n1.Experimental Validation of Simulation Results (Fig. 2): The manuscript would benefit from a more in-depth discussion of how the simulated light-induced phase transition pathways align with existing experimental observations. Are there published time-resolved studies such as ultrafast electron diffraction, X-ray diffraction, or transient absorption data, that support the key transitions proposed in Fig. 2? Discussing these connections will enhance the credibility and experimental relevance of the simulations.\n\n2. Phonon Mode Analysis and Raman Correlation (Fig. 4): The authors emphasize the role of specific phonon modes (e.g., B₃g₁) in driving the transition. It would be useful to discuss whether any ultrafast Raman spectroscopy studies (published or ongoing) support the appearance or evolution of such phonon modes under pulsed laser excitation. Can any characteristic Raman shifts be associated with the phonon activity simulated in Fig. 4?\n\n3. Cubic vs. Hexagonal Diamond Formation Conditions (Fig. 5): Under static HPHT conditions, it is well-known that hexagonal diamond tends to form at lower temperatures than cubic diamond. In Fig. 5, the light-induced phase diagram is intriguing, but lacks clear guidance on which laser parameters (e.g., fluence, pulse duration) favor hexagonal over cubic diamond. For experimentalists, a clearer interpretation of how these regimes are defined and how to tune laser conditions to selectively promote one phase over the other would greatly increase the practical utility of the figure.\n\n4. Clarification of Fig. S9: In the supplementary figure S9, the authors compare cases with Q = 0 and Q = 1. However, the text mentions Q = 0.75, which is not shown in the figure. Please clarify whether this case was simulated and if so, include it in the figure or explain its absence.\n\n5.Line 39 – Temperature-Dependent CD vs. HD Formation: The sentence referencing the temperature relationship between cubic and hexagonal diamond (CD and HD) formation needs clarification. Please revise for accuracy and consider citing experimental studies that establish this relationship under equilibrium conditions for comparison.", "reviewer_3": "This is a great work, very impressive and opening the doors to the future where diamond and other materials could be synthesized using lasers. The paper should be accepted. However, I have several questions that I hope can be addressed:\n\n1. What does 4% electronic excitation mean? 4 percent of 4 valence electrons per atom are excited?\n\n2. Simulations are done for a single crystal of graphite with a particular orientation of the polarization plane of the laser with respect to the crystal. How do the results translate to a polycrystal of graphite? Will more fluency be needed?\n\n3. Simulations are done in a small 16-atom cell. Can the authors estimate size effects? For once, diamond formation may be hindered by the interfacial energy. Other allotropes might appear too.\n\n4. For cold compression of graphite, the easiest allotrope to form is M-carbon (Li 2009; Boulfelfel 2012). Other candidates included carbon, bct4 carbon and dozens of other hypothetical forms (see paper by Haiyang Niu). Can the authors comment on their possibility to occur as a result of laser irradiation?\n\n5. I'm surprised that laser fluence monotonically decreases with wavelength. Surely this trend must break at some wavelength, otherwise very weak radiowaves would make diamond from graphite :)\n\n6. After electrons are excited to 2-4 eV above Fermi level, they should eventually relax back to the ground state, releasing energy as either light or more likely heat. So one will have very hot diamond at ambient pressure. Won't it revert back to graphite? This is what hot diamond usually does at ambient pressure.\n\nArtem R. Oganov", "reviewer_4": "This work has identified and is focussing on a timely and interesting topic. The authors use cutting-edge simulation techniques to compute electron dynamics and coupling of electron and phonons. In principle this work has the potential to be of interest to the audience of this journal, however, the current manuscript does not meet this standard. The work is exclusively computational and, while that itself is not a problem, the work does not rigorously address this scientific question.\n\nFirst, I suggest the authors start by a schematic and quantitative figures that captures the relevant processes. This should estimate energies and time scales for the crucial steps that are relevant here. Are the initial and final states, as well as the pathways that connect both, quantitatively reasonable? At the same time, routes towards computational or experimental validation of the provided results are necessary.\n\nSecond, the simulation techniques and involved approximations come with error bars that are absent in this work. This needs to be explained and quantified, to better understand what is relevant and what is the accuracy in this work. The physics present and absent in these simulations, due to the used approximations, need to be explained. It also is necessary to connect these error bars to possible experimental validation of these simulations. The chosen pulse parameters in this work should be connected to experimentally achievable pulse parameters and discussed explicitly in the paper.\n\nThird, I am wondering what technique is used to model electron-phonon coupling and how do the authors deal with the large difference in time scales between electrons and phonons.\n\nFourth, what is not clear to me is, is to which extent this work just presents a possible mechanism and what are other possible mechanisms. In real samples, many other effects contribute (defects, substrate, temperature, ...) and it is not clear to me, to what extent the idealized simulations here are providing a realistic picture that can be demonstrated in a real sample.\n\nAs it stands, I view the provided results as a proposal for a reaction mechanism, but that alone is not sufficient for the high standards of this journal."}, "author_response": "First of all, we would like to express our gratitude to all the four reviewers for valuable comments, which are very helpful for us to further improve the quality of the manuscript. We are also very pleased that all the four reviewers recognize the significance and high quality of our work. The reviewer’s comments are listed, followed by our responses and changes made in the revised manuscript.\n\nReviewer #1 (Remarks to the Author):\n[...]\nAuthor reply: We thank the reviewer for raising this important and insightful question. We agree with the reviewer that TDDFT calculations with conventional exchange-correlation functionals (e.g. ALDA) cannot perfectly describe the electron-electron scattering process. The approximate exchange-correlation functional may affect excitation energies and charge transfer rates. Compared to the actual situation, ALDA-TDDFT tends to underestimate the scatterings and energy transfer in real systems to some extent, as elucidated by Zhou, Lu and Prezhdo in Nano Lett. 21, 756, (2021). However, since we adopted the supercell calculations based on the multiple k points, some of the electron-electron scattering effects are naturally included in the localized regime due to the folding of k points. Moreover, electron-electron scattering mediated by the presence of lattice distortion (or virtual phonons) is also nicely incorporated in the present computational scheme. Therefore, while being fully respectful to the reviewer’s comments, we do believe that Auger process can be approximately tracked in the present simulation settings as shown in Fig. 3c.\n\nIn details, we analyzed the variation of charge carrier occupancy corresponding to each molecular orbitals during the photo-induced phase transition process. Fig. 3c presents the temporal evolution of the distribution of the photogenerated charge carriers within each orbital, which indicates a small fraction of photoexcited electrons is indeed scattered to high-energy orbitals during evolution of electron wavefunction. Such an increasing charge carrier distribution in high-energy orbitals can be understood with Auger recombination, where the excess energy released by electron-hole recombination scatters electrons to higher energy levels. We further emphasize that the focus of this work is to provide insights into the electronic driving forces underlying the graphite-to-diamond phase transition, rather than to quantitatively describe the Auger scattering and fully reproduce the corresponding experimental results. Previous study in Faraday Discuss. 224, 382 (2020) has also illustrated that when the natural occupation numbers remain close to their initial values, ALDA yields reasonably accurate electron density evolution.\n\nWe have incorporated further discussions on this point in the revised manuscript:\n“Since adiabatic TDDFT tends to underestimate the carrier-carrier interaction and the scattering rates in real systems to some extent42, the real electron-electron scattering effects may be more pronounced than indicated by the present simulation results.” (Main text page 8)\n\n2. In that context, have the authors checked whether the total energy (electrons plus nuclei) is conserved (at least up to 400 fs, before the dissipation sets in)?\n\nAuthor reply: We thank the reviewer for this good suggestion. Indeed, we have checked that during the application of the Gaussian light field, the total energy of the system oscillates and exhibits an overall increase, corresponding to the injection of laser energy into the system. After the end of light field irradiation, the total energy of the system remains essentially constant, with only a small drifting (~0.0002 eV/fs per atom), due to the accumulation of numerical errors. We have verified that this drift diminishes if an even smaller timestep is used.\n\nWe have added the following information in the Methods in the revised manuscript:\n“After the end of light field irradiation, the total energy of the system remains essentially constant, with only a slight drifting of ~0.0002 eV/fs per atom caused by the accumulation of numerical errors.” (Main text page 15)\n\n3. Also, the LDA gap of diamond is about 4.3 eV. The authors state that at 250 fs the gap is about 3.27 eV. Does the gap open up further after that?\n\nAuthor reply: Yes, we have checked that the diamond structure, following the 8-ps-long dynamical evolution, exhibits a further widened band gap of 3.63 eV. This structure is a diamond-like structure formed by the relaxation of a metastable excited-state phase-transition structure to 300 K (room temperature), and its band structure properties can be compared with those of the perfect cubic diamond at 0 K, as shown in Fig. 1R.\n\n[...]"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have substantially revised their manuscript in response to four referee reports. I believe that the paper has been much improved, and I am overall satisfied with the response of the authors to my own questions and comments. I think the authors also did a good job with the other three referee reports.\n\nOne point remains, namely the issue of the ALDA’s inability to properly describe the Auger effect. In the paper the authors just add the single short sentence “Since adiabatic TDDFT tends to underestimate the carrier-carrier interaction and the scattering rates in real systems to some extent^42, the real electron-electron scattering effects may be more pronounced than indicated by the present simulation results.”\n\nIn their rebuttal, the authors have made a convincing case that their approach at least includes electron-electron scattering to some degree, for instance due to their use of a supercell, and mediation via lattice distortions. Also, they found evidence by tracking orbital occupations. I would like to suggest to the authors to include a couple of brief additional sentences in the paper where these arguments are explicitly discussed, to justify that the Auger mechanism can be invoked here in spite of using ALDA.\n\nApart from this, the paper is now ready to be accepted.", "reviewer_2": "The authors answered all of my questions, and I suggest accepting current version of the manuscript.", "reviewer_3": "I am satisfied with the responses of the authors and their revision.\nThe paper can be accepted now.\nArtem R. Oganov", "reviewer_4": "The authors provided thoughtful answers to all reviewer questions. These answers, in particular those that connect the computational simulations and experiment, maintain my concern that the paper studies an interesting mechanism, but does not provide strong enough evidence that the simulations indeed study the previously reported situations. The conditions studied in this work are, in my opinion, far from experimentally achievable situations. The excitation of 4% seems huge, compared to what can be expected in experiment, without vaporizing the sample, if it can be achieved over significant volume (or surface) of the sample. Again, I think this is a very interesting model study, but it does not strongly enough connect experiment and theory and, thus, should be reported in a more specialized journal."}, "author_response": "First of all, we would like to express our gratitude to all reviewers for valuable comments during the previous round of review. These suggestions are very helpful for us to further improve the quality of the manuscript. We also thanks the reviewers for their recognition of the scientific merit of our work. The latest round of review comments are listed below, along with our responses and revisions made in the revised manuscript.\n\nReviewer #1 (Remarks to the Author):\n[...]\nAuthor reply: We greatly appreciate the reviewer's further valuable suggestions as well as the support and recognition for our work. Following the reviewer’s suggestion, we have incorporated further discussions on this point in the revised manuscript:\n“It is worth noting that although the Hamiltonian used in our non-adiabatic calculations does not explicitly include electron-electron scattering terms42, the incorporation of multiple k-points and the presence of lattice distortions (or virtual phonons) allow electron scattering to be included to a certain extent. This enables us to capture key Auger process and carrier transport. Since adiabatic TDDFT tends to underestimate the carrier-carrier interaction and the scattering rates in real systems to some extent, the real electron-electron scattering effects may be more pronounced than indicated by the present simulation results.” (Main text page 8)\n\nReviewer #3 (Remarks to the Author):\n[...]\nAuthor reply: We sincerely appreciate the reviewer for the support and recognition of our work. Their valuable suggestions have been of great help to us in improving the manuscript.\n\nReviewer #4 (Remarks to the Author):\n[...]\nAuthor reply: First and foremost, we sincerely appreciate the valuable time you have dedicated during the two rounds of review and the insightful questions you raised. These have inspired us to further enhance our technical capabilities in excited-state dynamics to better address the needs of practical research. It must be acknowledged that theoretical computation has its limitations, while current simulation methods are insufficient to fully replicate the complexity of real-world systems, and some degree of approximation is inevitable. However, we believe we have sufficiently recognized the limitations of these approximations and have strived to interpret our observations as objectively as possible, so as to avoid exaggerating or distorting the facts, and to prevent any potential misinterpretation by readers."}]

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