Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation

TL;DR

This paper explores a three-dimensional quantum Hall system with charge density modulation, revealing second-order topological phases with hinge modes and surface states that are controllable and robust.

Contribution

It introduces a new mechanism for realizing second-order topological phases with electrically switchable hinge modes in a 3D quantum Hall system.

Findings

Presence of chiral hinge modes dependent on CDW phase

Reversible hinge mode propagation via electrical control

Coexistence of 2D surface QHE states with hinge modes

Abstract

We consider a system of weakly coupled one-dimensional wires forming a three-dimensional stack in the presence of a spatially periodic modulation of the chemical potential along the wires, equivalent to a charge density wave (CDW). An external static magnetic field is applied parallel to the wire axes. We show that, for a certain parameter regime, due to interplay between the CDW and magnetic field, the system can support a second-order topological phase characterized by the presence of chiral quasi-1D Quantum Hall Effect (QHE) hinge modes. Interestingly, we demonstrate that direction of propagation of the hinge modes depends on the phase of the CDW and can be reversed only by electrical means without the need of changing the orientation of the magnetic field. Furthermore, we show that the system can also support 2D chiral surface QHE states, which can coexist with one-dimensional hinge modes, realizing a scenario of a hybrid high-order topology. We show that the hinge modes are robust against static disorder.