Quantum Hall Edge States in Topological Insulator Nanoribbons

TL;DR

This paper develops a microscopic theory for chiral edge states in topological insulator nanoribbons, explaining experimental transport phenomena in the quantum anomalous Hall regime.

Contribution

It introduces a continuum model for sidewall states in topological insulator nanoribbons, linking microscopic parameters to ribbon geometry and Fermi level positioning.

Findings

Number of chiral channels depends on ribbon thickness and Fermi level.

Theory explains non-zero longitudinal resistance in quantized Hall samples.

Model aligns with recent experimental observations.

Abstract

We present a microscopic theory of the chiral one-dimensional electron gas system localized on the sidewalls of magnetically-doped Bi$_2$Se$_3$-family topological insulator nanoribbons in the quantum anomalous Hall effect (QAHE) regime. Our theory is based on a simple continuum model of sidewall states whose parameters are extracted from detailed ribbon and film geometry tight-binding model calculations. In contrast to the familiar case of the quantum Hall effect in semiconductor quantum wells, the number of microscopic chiral channels depends simply and systematically on the ribbon thickness and on the position of the Fermi level within the surface state gap. We use our theory to interpret recent transport experiments that exhibit non-zero longitudinal resistance in samples with accurately quantized Hall conductances.