Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals

TL;DR

This paper investigates how disorder affects multi-gap Euler topological semimetals, revealing disorder-driven phase transitions, critical metallic phases, and the emergence of quantum anomalous Hall states, with implications for stability and universality of topological phases.

Contribution

It demonstrates the robustness of Euler topological phases under disorder, identifies universal critical exponents, and uncovers disorder-induced topological transitions to quantum anomalous Hall states.

Findings

Disorder drives Euler semimetals into critical metallic phases.

Universal localization length exponent of approximately 1.4 was found.

Magnetic disorder induces transitions to quantum anomalous Hall phases.

Abstract

We study the effect of disorder in systems having a non-trivial Euler class. As these recently proposed multi-gap topological phases come about by braiding non-Abelian charged band nodes residing between different bands to induce stable pairs within isolated band subspaces, novel properties may be expected. Namely, a~modified stability and critical phases under the unbraiding to metals can arise, when the disorder preserves the underlying $C_2\cal{T}$ or $\cal{P}\cal{T}$ symmetry on average. Employing elaborate numerical computations, we verify the robustness of associated topology by evaluating the changes in the average densities of states and conductivities for different types of disorders. Upon performing a scaling analysis around the corresponding quantum critical points we retrieve a universality for the localization length exponent of $\nu = 1.4 \pm 0.1$ for Euler-protected phases, relating to two-dimensional percolation models. We generically find that quenched disorder drives Euler semimetals into critical metallic phases. Finally, we show that magnetic disorder can also induce topological transitions to quantum anomalous Hall plaquettes with local Chern numbers determined by the initial value of the Euler invariant.