Phase transition between the quantum spin Hall and insulator phases in 3D: Emergence of a topological gapless phase

Abstract

Phase transitions between the quantum spin Hall (QSH) and the insulator phases in three dimensions (3D) are studied. We find that in inversionasymmetric systems there appears a gapless phase between the QSH and insulator phases in 3D which is in contrast with the 2D case. Existence of this gapless phase stems from a topological nature of gapless points (diabolical points) in 3D, but not in 2D. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.