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The IFCs calculated using the QE package [54] were determined with a Perdew-Zunger exchange-correlation functional and a von Barth-Car norm-conserving, scalar relativistic pseudopotential. A large vacuum space, 30 Å, was used between periodic layers to avoid interlayer interactions. The harmonic IFCs were calculated within DFPT using a 120 Ryd plane-wave cutoff and 13×13×1 (Equation presented)-point meshes for the electronic and phonon calculations [54, 55]
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The IFCs calculated using the QE package [54] were determined with a Perdew-Zunger exchange-correlation functional and a von Barth-Car norm-conserving, scalar relativistic pseudopotential. A large vacuum space, 30 Å, was used between periodic layers to avoid interlayer interactions. The harmonic IFCs were calculated within DFPT using a 120 Ryd plane-wave cutoff and 13×13×1 (Equation presented)-point meshes for the electronic and phonon calculations [54, 55]. The anharmonic IFCs were calculated out to fifth-nearest neighbors of the unit cell atoms with a real-space approach using Γ-point self-consistent calculations, a 162 atom supercell, and a 100 Ryd plane-wave cutoff. We note that the harmonic and anharmonic IFCs are well converged with a 100 Ryd plane-wave cutoff, thus increasing this value makes no difference in the calculations. Further, the calculation of (Equation presented) of unstrained graphene is converged by the fourth-nearest neighbor cutoff for the anharmonic IFCs. The calculated (Equation presented) values for unstrained graphene ((Equation presented) = 10 μm, (Equation presented) = 300 K) using anharmonic IFCs out to fifth-, sixth-, seventh-, and eighth-nearest neighbor cutoffs are all within 5% of the (Equation presented) value using a fourth-nearest neighbor cutoff. More details of the calculation of the anharmonic IFCs can be found in Refs. [41, 42, and 44]
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84899705223
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The ground state structure calculation employed a 6×6×1 (Equation presented)-point mesh, and the IFCs were determined from Γ-point self-consistent calculations with 128 atom supercells. The anharmonic IFCs were calculated out to tenth-nearest neighbor to the unit cell atoms. A vacuum space of 17 Å was used between periodic graphene layers. The VASP calculations of the unstrained IFCs were done independently of the QE calculations [56], thus different inputs were used. We note that despite differences in the calculations, both give similar (Equation presented), which demonstrates the robustness of the results
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The IFCs calculated using the VASP package [57] were determined with a Perdew-Burke-Ernzerhof exchange-correlation functional, a projector-augmented wave pseudopotential, and a 40 Ryd plane-wave cutoff. The ground state structure calculation employed a 6×6×1 (Equation presented)-point mesh, and the IFCs were determined from Γ-point self-consistent calculations with 128 atom supercells. The anharmonic IFCs were calculated out to tenth-nearest neighbor to the unit cell atoms. A vacuum space of 17 Å was used between periodic graphene layers. The VASP calculations of the unstrained IFCs were done independently of the QE calculations [56], thus different inputs were used. We note that despite differences in the calculations, both give similar (Equation presented), which demonstrates the robustness of the results
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The IFCs Calculated Using the VASP Package [57] Were Determined with A Perdew-Burke-Ernzerhof Exchange-correlation Functional, A Projector-augmented Wave Pseudopotential, and A 40 Ryd Plane-wave Cutoff
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