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

TL;DR

This study reveals that NaZnSb$_{1-x}$Bi$_x$ undergoes multiple topological phase transitions driven by composition changes, with mirror Chern numbers changing independently of symmetry indicators, highlighting complex topological behavior.

Contribution

The paper demonstrates topological phase transitions in NaZnSb$_{1-x}$Bi$_x$ driven by composition, with changes in mirror Chern numbers occurring without symmetry indicator signals, supported by first-principles calculations and a low-energy model.

Findings

Topological invariants change at specific compositions ($x$=0.15, 0.20, 0.53).

Mirror Chern numbers can change without symmetry indicators.

Spectator Dirac fermions influence topological transitions.

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.