Stable topological phase transitions without symmetry indications in NaZnSb${}_{1-x}$Bi${}_x$

Abstract

We study topological phase transitions in tetragonal NaZnSb${}_{1-x}$Bi${}_x$, driven by the chemical composition $x$. Notably, we examine mirror Chern numbers that change without symmetry indicators. First-principles calculations are performed to show that NaZnSb${}_{1-x}$Bi${}_x$ experiences consecutive topological phase transitions, diagnosed by the strong ${\mathbb{Z}}_2$ topological index ${\nu }_0$ and two mirror Chern numbers ${\mu }_x$ and ${\mu }_{xy}$. As the chemical composition $x$ increases, the topological invariants (${\mu }_x{\mu }_{xy}{\nu }_0$) change from $(000)$, $(020)$, $(220)$, to $(111)$ at $x$ = 0.15, 0.20, and 0.53, respectively. A simplified low-energy effective model is developed to examine the mirror Chern number changes, highlighting the central role of spectator Dirac fermions in avoiding symmetry indicators. Our findings suggest that NaZnSb${}_{1-x}$Bi${}_x$ can be an exciting testbed for the exploration of the interplay between the topology and symmetry.