Ballistic electron channels including weakly protected topological states in delaminated bilayer graphene

TL;DR

This paper investigates ballistic electron channels in delaminated bilayer graphene, revealing weakly protected topological states and their dependence on stacking order, delamination width, and electrostatic conditions through analytical and numerical methods.

Contribution

It introduces a detailed analysis of electron channels in delaminated bilayer graphene, highlighting the emergence of weakly topologically protected states and their dependence on stacking and electrostatic parameters.

Findings

Gapless channels in inverted stacking configurations

Gapped channels with gap scaling inversely with width and energy difference

Presence of multiple waveguide modes depending on delamination width

Abstract

We show that delaminations in bilayer graphene (BLG) with electrostatically induced interlayer asymmetry can provide one with ballistic channels for electrons with energies inside the electrostatically induced BLG gap. These channels are formed by a combination of valley-polarised evanescent states propagating along the delamination edges (which persist in the presence of a strong magnetic field) and standing waves bouncing between them inside the delaminated region (in a strong magnetic field, these transform into Landau levels in the monolayers). For inverted stacking between BLGs on the left and right of the delamination (AB-2ML-BA or BA-2ML-AB), the lowest energy ballistic channels are gapless, have linear dispersion and appear to be weakly topologically protected. When BLG stacking order on both sides of the delamination is the same (AB-2ML-AB or BA-2ML-BA), the lowest energy ballistic channels are gapped, with gap $\varepsilon_g$ scaling as $\varepsilon_g\propto W^{-1}$ with delamination width and as $\varepsilon_g\propto\delta^{-1}$ with the on-layer energy difference within the delamination. Depending on their width, delaminations may also support several `higher energy' waveguide modes. Our results are based on both an analytical study of the wavematching of Dirac states and tight binding model calculations, and we analyse in detail the dependence of the delamination spectrum on electrostatic conditions in the structure, such as the vertical displacement field.