Tuning phase transition between quantum spin Hall and ordinary insulating phases

2007/05/31 by Shuichi Murakami, Satoshi Iso, Y. Avishai +3 · 9 citations
Materials Science · Physics and Astronomy · #Graphene research and applications #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall #hep-th

paper · pdf · doi:10.1103/physrevb.76.205304

published as Phys.Rev.B76:205304,2007 · 6 pages, 2 figures, to appear in Phys. Rev. B

arxiv created 2007/10/11 · openalex publication_date 2007/11/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

An effective theory is constructed for analyzing a generic phase transition between the quantum spin Hall and the insulator phases. Occurrence of degeneracies due to closing of the gap at the transition are carefully elucidated. For systems without inversion symmetry the gap closing occurs at \ifmmode±\else\textpm\fi\stackrelPk₀(\ensuremath≠\stackrelPG∕2) while for systems with inversion symmetry, the gap can close only at wave numbers \stackrelPk=\stackrelPG∕2, where \stackrelPG is a reciprocal lattice vector. In both cases, following a unitary transformation which mixes spins, the system is represented by two decoupled effective theories of massive two-component fermions having masses of opposite signs. Existence of gapless helical modes at a domain wall between the two phases directly follows from this formalism. This theory provides an elementary and comprehensive phenomenology of the quantum spin Hall system.

Citations

• Topological Insulators with Inversion Symmetry
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Time Reversal Polarization and a Z₂ Adiabatic Spin Pump
• Spin-Hall Insulator
• Dissipationless Quantum Spin Current at Room Temperature

Cited by

• Effective continuous model for surface states and thin films of three-dimensional topological insulators
• Inversion-symmetric topological insulators
• Spin-orbit effects in a graphene bipolar pn junction
• Piezoelectricity and topological quantum phase transitions in two-dimensional spin-orbit coupled crystals with time-reversal symmetry
• Classification of Weyl points and nodal lines based on magnetic point groups for spin-(1)/(2) quasiparticles
• Massless Dirac fermions in III-V semiconductor quantum wells
• Topological invariants for interacting topological insulators with inversion symmetry
• Topological critical materials of ternary compounds
• Persistence of phase boundaries between a topological and trivialZ2insulator

Related

• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Spin-flip scattering at quantum Hall transition
• Bilayer Quantum Hall Systems: Spin-Pseudospin Symmetry Breaking and Quantum Phase Transitions
• Quantum spin Hall insulators with interactions and lattice anisotropy
• Theory of the Quantum Hall Insulator