Topological insulator: a new quantized spin Hall resistance robust to dephasing

TL;DR

This paper investigates the effects of dephasing on the quantum spin Hall effect, revealing that a newly defined spin Hall resistance exhibits robust quantum plateaus unaffected by dephasing, highlighting its topological nature.

Contribution

It introduces a new spin Hall resistance that remains quantized under dephasing, demonstrating robustness in macroscopic samples and advancing understanding of topological protection.

Findings

Quantum plateaus are robust against normal dephasing but fragile with spin dephasing.

Longitudinal resistance increases linearly with sample length, insensitive to width.

New spin Hall resistance exhibits quantum plateaus robust to all types of dephasing.

Abstract

The influence of dephasing on the quantum spin Hall effect (QSHE) is studied. In the absence of dephasing, the longitudinal resistance in a QSHE system exhibits the quantum plateaus. We find that these quantum plateaus are robust against the normal dephasing but fragile with the spin dephasing. Thus, these quantum plateaus only survive in mesoscopic samples. Moreover, the longitudinal resistance increases linearly with the sample length but is insensitive to the sample width. These characters are in excellent agreement with the recent experimental results [science {\bf 318}, 766 (2007)]. In addition, we define a new spin Hall resistance that also exhibits quantum plateaus. In particular, these plateaus are robust against any type of dephasing and therefore, survive in macroscopic samples and better reflect the topological nature of QSHE.