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

TL;DR

This paper presents a computational workflow to derive low-energy symmetric Hamiltonians and Hubbard parameters for twisted multilayer systems, demonstrated on twisted bilayer graphene, using ab-initio data and symmetry constraints.

Contribution

The work introduces a new efficient method to construct low-energy Hamiltonians and Hubbard parameters for twisted multilayer materials from ab-initio data.

Findings

Successfully applied to twisted bilayer graphene at the first magic angle.

Generated symmetry-respecting low-energy Hamiltonians with 4 and 12 bands.

Provided Hubbard parameters within the constrained random phase approximation.

Abstract

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 initial step, the full-energy tight-binding Hamiltonian is generated by the Slater-Koster model with parameters fitted to ab-initio data at larger angles. Then, the low-energy symmetric four-band and twelve-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 (cRPA) for screening, which again respect the symmetries. The relevant data and results of this work are freely available via an online repository. Our workflow, exemplified in this work on twisted bilayer graphene, is straightforwardly transferable to other twisted multi-layer materials.