An accurate tight binding model for twisted bilayer graphene describes topological flat bands without geometric relaxation

TL;DR

This paper introduces a precise tight binding model for twisted bilayer graphene that captures topological flat bands at magic angles without requiring geometric relaxation, revealing shifts in the magic angle and the emergence of fragile topology.

Contribution

The authors develop an accurate local environment tight binding model fitted to DFT calculations, showing flat bands and fragile topology without lattice relaxation.

Findings

Magic angle shifts to ~0.99° from 1.05°

Flat bands appear in rigidly rotated layers

Fragile topology emerges without lattice relaxation

Abstract

A major hurdle in understanding the phase diagram of twisted bilayer graphene (TBLG) are the roles of lattice relaxation and electronic structure on isolated band flattening near magic twist angles. In this work, the authors develop an accurate local environment tight binding model (LETB) fit to tight binding parameters computed from $ab\ initio$ density functional theory (DFT) calculations across many atomic configurations. With the accurate parameterization, it is found that the magic angle shifts to slightly lower angles than often quoted, from around 1.05$^\circ$ to around 0.99$^\circ$, and that isolated flat bands appear for rigidly rotated graphene layers, with enhancement of the flat bands when the layers are allowed to distort. Study of the orbital localization supports the emergence of fragile topology in the isolated flat bands without the need for lattice relaxation.