Nearly flat Chern band in periodically strained monolayer and bilayer graphene

TL;DR

This paper explores how periodic strain induces nearly flat, topologically nontrivial bands in monolayer and bilayer graphene, offering a platform for strongly correlated quantum states.

Contribution

It demonstrates the conditions for nearly flat bands in strained graphene and provides a topological and physical understanding of their origin.

Findings

Nearly flat topological bands with homogeneous Berry curvature in strained graphene.

Quantum metric of flat bands resembles Landau levels.

Strain acts as an effective gauge field in monolayer graphene, with a different role in bilayer graphene.

Abstract

The flat band is a key ingredient for the realization of interesting quantum states for novel functionalities. In this work, we investigate the conditions for the flat band in both monolayer and bilayer graphene under periodic strain. We find topological nearly flat bands with homogeneous distribution of Berry curvature in both systems. The quantum metric of the nearly flat band closely resembles that for Landau levels. For monolayer graphene, the strain field can be regarded as an effective gauge field, while for Bernal-stacked (AB-stacked) bilayer graphene, its role is beyond the description of gauge field. We also provide an understanding of the origin of the nearly flat band in monolayer graphene in terms of the Jackiw-Rebbi model for Dirac fermions with sign-changing mass. Our work suggests strained graphene as a promising platform for strongly correlated quantum states.