Construction of low-energy symmetric Hamiltonians and Hubbard parameters for twisted multilayer systems using ab initio input

A computationally efficient workflow for obtaining the low-energy symmetric tight-binding Hamiltonians for twisted multilayer systems is presented in this work. We apply this scheme to twisted bilayer graphene at the first magic angle. As the initial step, the full-energy tight-binding Hamiltonian is generated by the SlaterKoster model with parameters fitted to ab initio data at larger angles. Then, the low-energy symmetric four-band and 12-band Hamiltonians are constructed using the maximum-localization procedure subjected to crystal- and time-reversal-symmetry constraints. Finally, we compute extended Hubbard parameters for both models within the constrained random phase approximation for screening, which again respect the symmetries. Our workflow, exemplified in this work on twisted bilayer graphene, is straightforwardly transferable to other twisted multilayer materials.

Automated summary

This work presents a computationally efficient workflow for obtaining the low-energy symmetric tight-binding Hamiltonians for twisted multilayer systems. The workflow is applied to twisted bilayer graphene at the first magic angle. The full-energy tight-binding Hamiltonian is generated using the SlaterKoster model, and then the low-energy symmetric four-band and 12-band Hamiltonians are constructed using the maximum-localization procedure. Extended Hubbard parameters are computed within the constrained random phase approximation for screening. The workflow demonstrated on twisted bilayer graphene can be easily applied to other twisted multilayer materials.