Controlling edge states in the Kane-Mele model via edge chirality

TL;DR

This paper explores how the electronic properties of quantum spin Hall edge states in the Kane-Mele model depend on the crystallographic orientation of edges, revealing a monotonic increase in Fermi velocities from zigzag to armchair edges.

Contribution

It demonstrates the dependence of QSHE edge state dispersion on edge chirality and introduces an analytical model to explain this relationship.

Findings

Fermi velocities increase monotonically from zigzag to armchair edges.

QSHE edge states are present at all edge orientations with strong spin-orbit coupling.

An analytical model successfully explains the numerical results.

Abstract

We investigate the dependence of band dispersion of the quantum spin Hall effect (QSHE) edge states in the Kane-Mele model on crystallographic orientation of the edges. Band structures of the one-dimensional honeycomb lattice ribbons show the presence of the QSHE edge states at all orientations of the edges given sufficiently strong spin-orbit interactions. We find that the Fermi velocities of the QSHE edge-state bands increase monotonically when the edge orientation changes from zigzag (chirality angle $\theta = 0^\circ$) to armchair ($\theta = 30^\circ$). We propose a simple analytical model to explain the numerical results.