Density functional theory calculations of potential energy surface for commensurate moiré patterns of graphene

Density functional theory calculations are performed to investigate the potential energy surface (PES) for relative sliding of graphene layers forming (2,1) and (3,1) moiré patterns.The calculations are performed using the vdW-DF3 functional [1] as implemented in the Quantum Espresso code [2]. The calculations show that the PES is extremely flat with the amplitude of the corrugations on the order of 0.4 and 0.03 microeV per atom of one layer for the (2,1) and (3,1) patterns, respectively. Two types of constraints are applied to study the effect of structural relaxation: (1) fixing in-plane positions of all atoms (out-of-plane relaxation) and (2) only two atoms in the simulation cell. It is found that the account of structural relaxation doubles the amplitude of PES corrugations for the (2,1) pattern, while causing only minimal changes for the (3,1) pattern. The results for aligned layers are also included for comparison. The dependence of the energies of symmetric stackings on the interlayer distance is computed for the vdW-DF3 and PBE functions to analyze the differences in the interlayer interaction for twisted and aligned graphene layers. [1] D. Chakraborty, K. Berland, and T. Thonhauser, J. Chem. Theory and Computation 16, 5893 (2020). [2] P. Giannozzi, et al. J. Chem. Phys. 152, 154105 (2020). The data are organized as follows: qe-vdw-df3-bond.tar.gz - geometry optimization of a single graphene layer, qe-aligned* - calculations for aligned graphene layers, qe-21-vdw-df3* - calculations for the (2,1) moiré pattern using the vdW-DF3 functional, qe-21-pbe* - calculations for the (2,1) moiré pattern using the PBE functional, qe-31-vdw-df3* - calculations for the (3,1) moiré pattern using the vdW-DF3 functional, etc.