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

Understand

Phase transitions between the quantum spin Hall and the insulator phases in three dimensions are studied.

• We find that in inversion-asymmetric systems there appears a gapless phase between the quantum spin Hall and insulator phases in three dimensions, which is in contrast with the two-dimensional case.
• Existence of this gapless phase stems from a topological nature of gapless points (diabolical points) in three dimensions, but not in two dimensions.