Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene

TL;DR

This paper constructs a low-energy effective model for twisted bilayer graphene using maximally localized Wannier orbitals, revealing unique orbital structures and potential for unconventional many-body states.

Contribution

It introduces a novel Wannier orbital construction for twisted bilayer graphene and derives an extended Hubbard model capturing its low-energy physics.

Findings

Wannier orbitals have a three-peak structure at triangle corners

Estimated Coulomb and exchange interactions between Wannier states

Charge-ordered and homogeneous states have similar Coulomb energies at two electrons per supercell

Abstract

We develop an effective extended Hubbard model to describe the low-energy electronic properties of the twisted bilayer graphene. By using the Bloch states in the effective continuum model and with the aid of the maximally localized algorithm, we construct the Wannier orbitals and obtain an effective tight-binding model on the emergent honeycomb lattice. We found the Wannier state takes a peculiar three-peak form in which the amplitude maxima are located at the triangle corners surrounding the center. We estimate the direct Coulomb interaction and the exchange interaction between the Wannier states. At the filling of two electrons per super cell, in particular, we find an unexpected coincidence in the direct Coulomb energy between a charge-ordered state and a homogeneous state, which would possibly lead to an unconventional many-body state.