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 (15)

• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Effect in Silicene
• Anderson Transitions
• Low-energy effective Hamiltonian involving spin-orbit coupling in Silicene and Two-Dimensional Germanium and Tin
• Electrically Tunable Band Gap in Silicene
• Topological Insulator and Helical Zero Mode in Silicene under Inhomogeneous Electric Field
• Valley-Spin Polarization in the Magneto-Optical Response of Silicene and Other Similar 2D Crystals
• Valley polarized quantum Hall effect and topological insulator phase transitions in silicene
• Magneto-Optical Conductivity of Silicene and Other Buckled Honeycomb Lattices
• 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
• Searching for pairing energies in phase space

Cited by in corpus (21)

• Band inversion at critical magnetic fields in a silicene quantum dot
• Non-trivial topology of the quasi-one-dimensional triplons in the quantum antiferromagnet ${\text{BiCu}}_2{\text{PO}}_6$
• Topological Corner States in Graphene by Bulk and Edge Engineering
• Unscrambling of single-particle wave functions in systems localized through disorder and monitoring
• Delocalization of edge states in topological phases
• Entanglement production by statistical operators
• Hilbert space structure of the low energy sector of U(N) quantum Hall ferromagnets and their classical limit
• Magnetic Field Controlled Surface Localization of Spin-Wave Ferromagnetic Resonance Modes in 3D Nanostructures
• Faraday rotation and transmittance as markers of topological phase transitions in 2D materials
• Light-cone and local front dynamics of a single-particle extended quantum walk
• Some properties of Grassmannian $U(4)/U(2{)}^2$ coherent states and an entropic conjecture
• Capturing magic angles in twisted bilayer graphene from information theory markers
• Phase Crossover induced by Dynamical Many Body Localization in Periodically Driven Long-Range Spin Systems
• Quantum revivals in HgTe/CdTe quantum wells and topological phase transitions
• 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
• Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field
• The Photochemical Birth of the Hydrated Electron in Liquid Water
• Equilibration and Typicality in Quantum Processes
• Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model
• Localization and entanglement characterization of edge states in HgTe quantum wells in a finite strip geometry