Identifying topological-band insulator transitions in silicene and other 2D gapped Dirac materials by means of R\'enyi-Wehrl entropy

TL;DR

This paper introduces a novel entropy-based method using Rnyi-Wehrl entropy to detect topological phase transitions in silicene and similar 2D gapped Dirac materials under magnetic and electric fields.

Contribution

It presents a new entropic approach to identify topological-insulator to band-insulator transitions in 2D Dirac materials, applicable to systems with strong spin-orbit coupling.

Findings

Electron-hole entropies cross at charge neutrality point.

Maximum combined entropy indicates critical transition point.

Method applicable to general 2D gapped Dirac materials.

Abstract

We propose a new method to identify transitions from a topological insulator to a band insulator in silicene (the silicon equivalent of graphene) in the presence of perpendicular magnetic and electric fields, by using the R\'enyi-Wehrl entropy of the quantum state in phase space. Electron-hole entropies display an inversion/crossing behavior at the charge neutrality point for any Landau level, and the combined entropy of particles plus holes turns out to be maximum at this critical point. The result is interpreted in terms of delocalization of the quantum state in phase space. The entropic description presented in this work will be valid in general 2D gapped Dirac materials, with a strong intrinsic spin-orbit interaction, isoestructural with silicene.