Chiral and Non-Chiral Edge States in Quantum Hall Systems with Charge Density Modulation

TL;DR

This paper explores how charge density wave modulations influence edge states in quantum Hall systems, revealing a tunable transition between topological and non-topological phases with distinct edge state properties.

Contribution

It demonstrates the control of topological phases in quantum Hall systems via charge density modulation, providing analytical and numerical insights into edge state robustness.

Findings

Transition between topological and non-topological phases controlled by modulation amplitude ratio.

Edge states are robust to disorder, with topological phase states immune to phase shift disorder.

Analytical solutions for filling factor ν=1 and numerical results for higher filling factors.

Abstract

We consider a system of weakly coupled wires with quantum Hall effect (QHE) and in the presence of a spatially periodic modulation of the chemical potential along the wire, equivalent to a charge density wave (CDW). We investigate the competition between the two effects which both open a gap. We show that by changing the ratio between the amplitudes of the CDW modulation and the tunneling between wires, one can switch between non-topological CDW-dominated phase to topological QHE-dominated phase. Both phases host edge states of chiral and non-chiral nature robust to on-site disorder. However, only in the topological phase, the edge states are immune to disorder in the phase shifts of the CDWs. We provide analytical solutions for filling factor $\nu=1$ and study numerically effects of disorder as well as present numerical results for higher filling factors.