Fig. 2. Universal phase diagram for ℤ₂ topological phase transitions and evolutions of the band structure upon the transition.

(A) Universal phase diagram for ℤ₂ topological phase transitions. It is shown as a function of an external parameter, m, and a parameter δ controlling a degree of inversion symmetry breaking (1). The horizontal dashed line is the inversion-symmetric line. (B and C) Evolutions of bulk band structure with a change of the parameter m for inversion-symmetric (B) and inversion-asymmetric (C) cases, respectively. The blue and the red arrows in (A) correspond to the cases (B) and (C), respectively. DSM represents a Dirac semimetal.