# Emergent $Z_2$ Topological Invariant and Robust Helical Edge States in Two-Dimensional Topological Metals

## TL;DR

This paper predicts that disorder can induce a quantum spin Hall phase with robust helical edge states in two-dimensional topological metals, even without a global band gap, revealing new topological phenomena in metallic systems.

## Contribution

It introduces an emergent $Z_2$ topological invariant that protects helical edge states in disordered topological metals, enabling QSH phases without a global band gap.

## Key findings

- Disorder induces robust helical edge states in topological metals.
- Emergent $Z_2$ invariant protects edge states without a global gap.
- Quantized conductance plateau observed in transport simulations.

## Abstract

In this work, we study the disorder effect on topological metals that support a pair of helical edge modes deeply embedded inside the gapless bulk states. Strikingly, we predict that a quantum spin Hall (QSH) phase can be obtained from such topological metals without opening a global band gap. To be specific, disorder can lead to a pair of robust helical edge states which is protected by an emergent $Z_2$ topological invariant, giving rise to a quantized conductance plateau in transport measurements. These results are instructive for solving puzzles in {various transport experiments on QSH materials} that are intrinsically metallic. This work also will inspire experimental realization of the QSH effect in disordered topological metals.