# Electric Field-Defined Superlattices in Bilayer Graphene: Formation of Topological Bands in Two Dimensions

## TL;DR

Applying electric fields to bilayer graphene creates new topological electronic states with potential for controlling material properties.

## Contribution

The discovery of two-dimensional topological gapless states in bilayer graphene through electric field-defined superlattices.

## Key findings

- Electric field walls in bilayer graphene generate chiral gapless states that form minibands.
- Miniband crossings at the Fermi level create Dirac-like cones with topological character.
- Changing field polarization can switch the superlattice from semiconducting to metallic.

## Abstract

An electric field applied to the Bernal-stacked bilayer graphene opens an energy gap; its reversal in some regions creates domain walls and leads to the appearance of one-dimensional chiral gapless states localized at the walls. Here, we investigate the energy structure of bilayer graphene with superlattice potential defined by an external electric field. The calculations are performed within an atomistic π-electron tight-binding approximation. We study one-dimensional and two-dimensional superlattices formed by arrays of electric-field walls in the zigzag and armchair directions and investigate different field polarizations. Chiral gapless states discretize due to the superlattice potential and transform into minibands in the energy gap. As the main result, we show that the minibands can cross at the Fermi level for some field polarizations. This leads to a new kind of two-dimensional gapless states of topological character that form Dirac-like cones at the crossing points. This also has application potential: changing the field polarization can close the energy gap and change the character of the superlattice from semiconducting to metallic.