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.

arXiv comment6+11 pages, 4+9 figures

References in corpus (67)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Topological Insulators
• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Insulators with Inversion Symmetry
• Electronic transport in two dimensional graphene
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Classification of topological quantum matter with symmetries
• Experimental discovery of Weyl semimetal TaAs
• Topological quantum chemistry
• Kwant: a software package for quantum transport
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal NbP
• The Kernel Polynomial Method
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Scaling Theory of the Integer Quantum Hall Effect
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Discovery of Weyl fermion semimetals and topological Fermi arc states
• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• Mapping topological order in coordinate space
• Disclination Loops, Hedgehogs, and All That
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Non-Abelian band topology in noninteracting metals
• Non-Abelian reciprocal braiding of Weyl points and its manifestation in $\text{ZrTe}$
• Quasiparticle interference of the Fermi arcs and surface-bulk connectivity of a Weyl semimetal
• Quantum transport of disordered Weyl semimetals at the nodal point
• Topological Euler class as a dynamical observable in optical lattices
• Experimental observation of non-Abelian topological charges and bulk-edge correspondence
• Observation of non-Abelian topological semimetals and their phase transitions
• Dual gauge field theory of quantum liquid crystals in two dimensions
• Geometric approach to fragile topology beyond symmetry indicators
• Real-space calculation of the conductivity tensor for disordered topological matter
• Average Symmetry-Protected Topological Phases
• Dirty Weyl semimetals: Stability, phase transition and quantum criticality
• Rare region induced avoided quantum criticality in disordered three-dimensional Dirac and Weyl semimetals
• Intrinsic axion insulating behavior in antiferromagnetic MnBi${}_6$Te${}_{10}$
• Topological correspondence between magnetic space group representations
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• The translational side of topological band insulators
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Orbital Magnetization as a Local Property
• Topological Marker Currents in Chern Insulators
• Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node
• Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality
• Dissolution of topological Fermi arcs in a dirty Weyl semimetal
• Holography of the Dirac Fluid in Graphene with two currents
• Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
• Four-band non-Abelian topological insulator and its experimental realization
• Locality of the anomalous Hall conductivity
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Computation of topological phase diagram of disordered Pb${}_{1-x}$Sn${}_x$Te using the kernel polynomial method
• Subdimensional topologies, indicators and higher order phases
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Delocalization Transition of Disordered Axion Insulator
• Generalized liquid crystals: giant fluctuations and the vestigial chiral order of $I$, $O$ and $T$ matter
• Topological continuum charges of acoustic phonons in 2D
• Non-Abelian tensor Berry connections in multi-band topological systems
• Phase transitions of non-Abelian charged nodal links in a spring-mass system
• Classification of point-group-symmetric orientational ordering tensors
• Landau Levels of the Euler Class Topology
• Standard Model as the topological material
• Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry

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