Asymmetry gap in the electronic band structure of bilayer graphene

TL;DR

This paper models how an external electric field creates an asymmetry gap in bilayer graphene's electronic structure, affecting its quantum Hall properties and showing how screening influences the gap and electron density.

Contribution

It introduces a self-consistent Hartree approach to describe the density-dependent asymmetry gap in bilayer graphene under external electric fields.

Findings

The asymmetry gap $\

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Abstract

A tight binding model is used to calculate the band structure of bilayer graphene in the presence of a potential difference between the layers that opens a gap $\Delta$ between the conduction and valence bands. In particular, a self consistent Hartree approximation is used to describe imperfect screening of an external gate, employed primarily to control the density $n$ of electrons on the bilayer, resulting in a potential difference between the layers and a density dependent gap $\Delta (n)$. We discuss the influence of a finite asymmetry gap $\Delta (0)$ at zero excess density, caused by the screening of an additional transverse electric field, on observations of the quantum Hall effect.