Minimum model for the electronic structure of twisted bilayer graphene and related structures

TL;DR

This paper presents a minimal tight-binding model with three parameters that accurately captures the electronic properties of twisted bilayer graphene, untwisted bilayer graphene, and related layered materials, including the magic angle phenomena.

Contribution

A simple, parameter-efficient model that reproduces the electronic structure of twisted bilayer graphene and similar systems, facilitating future studies.

Findings

Accurately reproduces electronic structures near the Fermi level.

Captures the magic angle and associated flat bands.

Applicable to various twisted layered materials.

Abstract

We introduce a minimum tight-binding model with only three parameters extracted from graphene and untwisted bilayer graphene. This model reproduces quantitatively the electronic structure of not only these two systems and bulk graphite near the Fermi level, but also that of twisted bilayer graphene including the value of the magic angle, at which bands at $E_F$ flatten without overlap and two gaps open, one above and one below $E_F$. The Hamiltonian is sufficiently transparent and flexible to be adopted to other twisted layered systems.