The topological system with a twisting edge band: position-dependent Hall resistance

TL;DR

This paper investigates a novel topological system with a twisting edge band, revealing that its Hall resistance varies with measurement position due to the coexistence of protected and unprotected edge states, unlike standard topological insulators.

Contribution

It introduces a topological system featuring a twisting edge band with position-dependent Hall resistance, highlighting the coexistence of protected and unprotected edge states.

Findings

Hall resistance depends on measurement location.

System has both protected and unprotected edge states.

Unique position-dependent topological property identified.

Abstract

We study a $\nu=1$ topological system with one twisting edge-state band and one normal edge-state band. For the twisting edge-state band, Fermi energy goes through the band three times, thus, having three edge states on one side of the sample; while the normal edge band contributes only one edge state on the other side of the sample. In such a system, we show that it consists of both topologically protected and unprotected edge states, and as a consequence, its Hall resistance depends on the location where the Hall measurement is done even for a translationally invariant system. This unique property is absent in a normal topological insulator.