Total energy of twisted bilayer graphene from a tight binding model
Phys. Rev. B 114, 065125 – Published 20 July, 2026
DOI: https://doi.org/10.1103/j9sg-gbth
Abstract
We present a semiempirical total-energy tight binding (TETB) parametrization for bilayer graphene that is transferable to arbitrary interlayer separation and local disregistry, and therefore to arbitrary interlayer twist angle. We use this model to investigate how tight binding forces influence the relaxed structures of twisted bilayer graphene (tBLG). The TETB model uses existing Slater-Koster style distance-dependent tight binding parameters to represent the electronic contribution to the energy. In order to capture the remaining contributions to the total energy, we define residual potentials—classical interatomic potentials that, when added to the tight binding band energy of a system, allow us to recreate a potential energy surface of arbitrary interlayer separation and local disregistry. We fit the residual potentials to diffusion quantum Monte Carlo (QMC) and density functional theory (DFT) total-energy data for a range of disregistries, interlayer separations, and biaxial strains. The resulting parametrization enables large-scale calculations (tens of thousands of atoms) with QMC-accurate total energies and built-in electronic structure dependence. As a demonstration, the models are used to relax tBLG with twist angles as low as , with unit cells containing as many as 16 876 atoms. At this scale, the relaxations are orders of magnitude faster than recent DFT results. We find that structures relaxed with the TETB model differ from structures relaxed using a reactive bond order (REBO) potential plus Kolmogorov-Crespi classical potential, despite both models being fit to the same total-energy data. These structural differences lead to differences in band structures and even magic angles. We find that the TETB model has a negative out-of-plane Poisson ratio, comparable to results obtained by DFT, whereas the classical model has a Poisson ratio close to zero. Given the differences in out-of-plane Poisson ratio, we show that in-plane biaxial strain has little effect on the magic angle in TETB-relaxed structures but significantly affects the magic angle in structures relaxed with the classical model. We conclude that the difference in magic angle behavior is due to the inclusion of tight binding forces in the relaxation method.
