Tuning phase transition between quantum spin Hall and ordinary insulating phases

Shuichi Murakami, Satoshi Iso, Yshai Avishai, Masaru Onoda, Naoto Nagaosa

Research output: Contribution to journalArticlepeer-review

142 Scopus citations


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 ± k 0 (≠ G /2) while for systems with inversion symmetry, the gap can close only at wave numbers k = G /2, where G 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.

Original languageEnglish
Article number205304
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number20
StatePublished - 2 Nov 2007

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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