Influence of minivalleys and Berry curvature on electrostatically induced quantum wires in gapped bilayer graphene

TL;DR

This paper investigates how minivalleys and Berry curvature influence the electronic spectrum and conductance in electrostatically defined quantum wires in gapped bilayer graphene, revealing valley-dependent degeneracies and magnetic field effects.

Contribution

It demonstrates the direct manifestation of minivalley structure and Berry curvature effects in the subband spectrum and magneto-conductance of bilayer graphene quantum wires, highlighting valley splitting phenomena.

Findings

Degeneracies of low-energy minibands reflect minivalley structure.

Magnetic field induces linear valley splitting.

Conductance steps vary with channel width and magnetic field.

Abstract

We show that the spectrum of subbands in an electrostatically defined quantum wire in gapped bilayer graphene directly manifests the minivalley structure and reflects Berry curvature via the associated magnetic moment of the states in the low-energy bands of this two-dimensional material. We demonstrate how these appear in degeneracies of the low-energy minibands and their valley splitting, which develops linearly in a weak magnetic field. Consequently, magneto-conductance of a ballistic point contact connecting two non-gapped areas of a bilayer through a gapped (top and bottom gated) barrier would reflect such degeneracies by the heights of the first few conductance steps developing upon the increase of the doping of the BLG conduction channel: $8e^2/h$ steps in a wide channel in BLG with a large gap, $4e^2/h$ steps in narrow channels, all splitting into a staircase of $2e^2/h$ steps upon lifting valley degeneracy by a magnetic field.