Theory of engineering flat bands in graphene using doubly-periodic electrostatic gating

TL;DR

This paper investigates how doubly periodic electrostatic potentials, especially Kagome patterns, can be used to engineer flat electronic bands in graphene, opening new avenues for graphene-based metamaterials.

Contribution

It demonstrates that specific doubly periodic electrostatic potentials can effectively induce flat bands in graphene, providing a novel method for band structure engineering.

Findings

Kagome potential best induces band flattening

Flat bands achieved with realistic potential parameters

Electrostatic gating enables band structure control in graphene

Abstract

We explore the use of applied electrical potentials to induce band flattening in graphene for bands near zero energy. We consider various families of doubly periodic potentials and simulate their effect on the electronic band structure using a tight-binding and a continuum approach. From these families, we find that an applied potential with symmetries of wallpaper group 17, in particular a Kagome potential, works best for inducing a high degree of band flattening for a range of realistic potential amplitudes and periods. Our work indicates that it should be possible to engineer the band structure of graphene using electrostatic gating, thus enabling a new approach to the development of graphene-based metamaterials.