Inverse participation ratio and localization in topological insulator phase transitions

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.

References in corpus (7)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Anderson Transitions
• Valley polarized quantum Hall effect and topological insulator phase transitions in silicene
• Husimi distribution and phase space analysis of Dicke model quantum phase transition
• Husimi distribution and phase-space analysis of a vibron-model quantum phase transition
• Identifying topological-band insulator transitions in silicene and other 2D gapped Dirac materials by means of Rényi-Wehrl entropy
• Entropic uncertainty relations and topological-band insulator transitions in 2D gapped Dirac materials

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• Phase Crossover induced by Dynamical Many Body Localization in Periodically Driven Long-Range Spin Systems
• Capturing magic angles in twisted bilayer graphene from information theory markers
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• Topological Properties of Single-Particle States Decaying into a Continuum due to Interaction
• Multifractality and excited-state quantum phase transition in ferromagnetic spin-$1$ Bose-Einstein condensates
• The Photochemical Birth of the Hydrated Electron in Liquid Water
• Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model
• Equilibration and Typicality in Quantum Processes
• Localization and entanglement characterization of edge states in HgTe quantum wells in a finite strip geometry