Topological phase transitions without symmetry indication in NaZnSb _1-x Bi _x

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 ℤ_2 topological index ν _0 and two mirror Chern numbers μ _x and μ _xy . As the chemical composition x increases, the topological invariants ( μ _xμ _xyν _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 exploring the interplay between the topology and symmetry.