Unconventional topological phase transition in non-symmorphic material KHgX (X = As, Sb, Bi)

Traditionally topological phase transition describes an evolution from topological trivial to topological nontrivial state. Originated from the non-symmorphic crystalline symmetry, we propose in this work an unconventional topological phase transition scheme between two topological nontrivial insulating states mediated by a Dirac gapless state, differing from the traditional topological phase transition. The KHgX (X = As, Sb, Bi) family is the first experimentally realized topological non-symmorphic crystalline insulator (TNCI), where the topological surface states are characterized by the Mobius-twisted connectivity. Based on first-principles calculations, we present a topological insulator-metal transition from TNCI into a Dirac semimetal (DSM) via applying an external pressure on KHgX. We find an unusual mirror Chern number C-m = -3 for the DSM phase of KHgX in the non-symmorphic crystal structure, which is topologically distinct from the traditional DSM such as Na3Bi and Cd3As2. Furthermore, we predict a new TNCI phase in KHgX via symmetry breaking. The topological surface states in this new TNCI phase display zigzag connectivity, different from the unstressed one. Our results offer a comprehensive study for understanding how the topological surface states evolve from a quantum phase transition in non-symmorphic system.