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

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 $C_2\mathcal{T}$ or $\mathcal{P}\mathcal{T}$ 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.

6+11 pages, 4+9 figures

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Cited by in corpus (9)

• Quantized Integrated Shift Effect in Multigap Topological Phases
• Optical manifestations and bounds of topological Euler class
• Anomalous geometric transport signatures of topological Euler class
• Optical signatures of Euler superconductors
• Floquet non-Abelian topological charges and edge states
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Emergence of Nodal-Knot Transitions by Disorder
• Hinge modes of three-dimensional Euler insulators