Inverse participation ratio and localization in topological insulator phase transitions

TL;DR

This paper demonstrates that the inverse participation ratio (IPR) effectively characterizes topological insulator transitions in 2D Dirac materials like silicene, enabling the definition of topological quantum numbers through IPR behavior.

Contribution

It introduces a novel use of IPR fluctuations to identify and distinguish topological and band insulator phases in 2D Dirac materials.

Findings

IPR characterizes topological phase transitions in silicene.

Topological-like quantum numbers are defined via IPR as a function of electric field.

Distinct IPR values correspond to different topological phases.

Abstract

Fluctuations of Hamiltonian eigenfunctions, measured by the inverse participation ratio (IPR), turn out to characterize topological-band insulator transitions occurring in 2D Dirac materials like silicene, which is isostructural with graphene but with a strong spin-orbit interaction. Using monotonic properties of the IPR, as a function of a perpendicular electric field (which provides a tunable band gap), we define topological-like quantum numbers that take different values in the topological-insulator and band-insulator phases.