Localization in a quantum spin Hall system

TL;DR

This paper investigates electronic state localization in a two-dimensional quantum spin Hall system, revealing unique phase transitions and critical behavior linked to its topological properties.

Contribution

It provides the first detailed phase diagram and critical exponent analysis for localization in a QSH system, highlighting its distinct universality class.

Findings

Phase diagram shows levitation and pair-annihilation of extended states.

Critical exponent for localization length divergence is approximately 1.6.

QSH system exhibits a different universality class from conventional quantum Hall systems.

Abstract

Localization problem of electronic states in a two-dimensional quantum spin Hall system (QSH - a symplectic model with a non-trivial topological structure) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair-annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent $\nu$ for the divergence of the localization length is estimated as $\nu \cong 1.6$ which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. This strongly suggests a different universality class related to the non-trivial topology of the QSH system.