Topological phase transitions without symmetry indication in NaZnSb $$_{1-x}$$ 1 - x Bi $$_x$$ x

Abstract

Abstract We study topological phase transitions in tetragonal NaZnSb $$_{1-x}$$ 1 - x Bi $$_x$$ 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 $$_{1-x}$$ 1 - x Bi $$_x$$ x experiences consecutive topological phase transitions, diagnosed by the strong $${\mathbb {Z}}_2$$ Z 2 topological index $$\nu _{0}$$ ν 0 and two mirror Chern numbers $$\mu _{x}$$ μ x and $$\mu _{xy}$$ μ xy . As the chemical composition x increases, the topological invariants ( $$\mu _{x}\mu _{xy}\nu _{0}$$ μ x μ xy ν 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 $$_{1-x}$$ 1 - x Bi $$_{x}$$ x can be an exciting testbed for exploring the interplay between the topology and symmetry.