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.

传统的拓扑相变描述了从拓扑琐碎状态到拓扑非琐碎状态的演变。源于非对称晶体对称性，我们在这项工作中提出了一种由狄拉克无隙态介导的，与传统拓扑相变不同的两个拓扑非平凡绝缘态之间的非常规拓扑相变方案。KHgX（X = As，Sb，Bi）系列是第一个通过实验实现的拓扑非对称结晶绝缘体（TNCI），其拓扑表面状态以莫比乌斯扭曲的连通性为特征。基于第一性原理计算，我们通过在KHgX上施加外部压力，介绍了从TNCI到狄拉克半金属（DSM）的拓扑绝缘体-金属过渡。我们发现一个不寻常的镜像陈恩数 在非同形晶体结构中，KHgX的DSM相的C _m = -3，这与传统的DSM（例如Na ₃ Bi和Cd ₃ As _2）在拓扑上是不同的。此外，我们通过对称破坏预测了KHgX中新的TNCI相。在这个新的TNCI相中，拓扑表面状态显示为锯齿形连通性，与未受应力的状态不同。我们的结果为理解拓扑表面状态如何从非对称系统中的量子相变演化提供了全面的研究。