Band gaps in graphene via periodic electrostatic gating

TL;DR

This study demonstrates that periodic electrostatic gating can induce a band gap in graphene, but the gap size is limited and sensitive to the gating potential's geometry and smoothness, contrasting with prior Dirac equation predictions.

Contribution

It reveals that electrostatic gating can open a band gap in graphene, providing insights into the dependence on geometry and potential smoothing, which was not previously well understood.

Findings

Electrostatic gating can open a band gap in graphene.

The band gap size is smaller compared to perforated graphene structures.

Smoothing the gate potential significantly reduces the attainable band gap.

Abstract

Much attention has been focused on ways of rendering graphene semiconducting. We study periodically gated graphene in a tight-binding model and find that, contrary to predictions based on the Dirac equation, it is possible to open a band gap at the Fermi level using electrostatic gating of graphene. However, comparing to other methods of periodically modulating graphene, namely perforated graphene structures, we find that the resulting band gap is significantly smaller. We discuss the intricate dependence of the band gap on the magnitude of the gate potential as well as the exact geometry of the edge of the gate region. The role of the overlap of the eigenstates with the gate region is elucidated. Considering more realistic gate potentials, we find that introducing smoothing in the potential distribution, even over a range of little more than a single carbon atom, reduces the attainable band gap significantly.