Topological and conventional phases of a three dimensional electron glass

Abstract

We investigate a symmetry protected $Z_2$ topological electron glass -- a glassy equivalent of the $Z_2$ topological band insulator in crystalline systems -- and uncover associated quantum phase transitions in this three dimensional amorphous network of atoms. Through explicit numerical calculations of the Witten effect, we show that the $Z_2$ glass is characterized by an anomalous electromagnetic response -- dyons with 1/2 electronic charge. We further study, using a variety of numerical diagnostics including such electromagnetic responses, the phase transitions of the $Z_2$ glass into a metallic and/or a trivial insulating phase. We find that the phase transitions here are governed by subtle features of mobility edges and "spectral inversion" which are possibly unique to structurally amorphous systems. Our results provide a concrete setting to understand the general underpinnings of such phases -- where strong structural disorder interplays with symmetry-protected topological order.

arXiv comment8 pages, 9 figures

References in corpus (48)

• Topological Insulators
• Topological insulators and superconductors
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Anderson Transitions
• Topological Insulator Materials
• The (High Quality) Topological Materials In The World
• Zoo of quantum-topological phases of matter
• Scaling Theory of the Integer Quantum Hall Effect
• Topological Anderson Insulator
• Amorphous topological insulators constructed from random point sets
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Classification of interacting electronic topological insulators in three dimensions
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Topological Insulators in Random Lattices
• Topological Anderson Insulator in Three Dimensions
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
• Fractional topological insulators in three dimensions
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Correlated Topological Insulators and the Fractional Magnetoelectric Effect
• K-Theory and Pseudospectra for Topological Insulators
• Topological phases: Classification of topological insulators and superconductors of non-interacting Fermions, and beyond
• Witten effect in a crystalline topological insulator
• Disordered weak and strong topological insulators
• Fractionalized Topological Insulators
• Topological insulators beyond the Brillouin zone via Chern parity
• Topological Amorphous Metals
• Disorder effect on 3-dimensional $Z_2$ quantum spin Hall systems
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
• A noncommutative framework for topological insulators
• A Computational Non-Commutative Geometry Program for Disordered Topological Insulators
• Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant
• Criticality of the metal-topological insulator transition driven by disorder
• Topological invariant in three-dimensional band insulators with disorder
• Global phase diagram of a three dimensional dirty topological superconductor
• Topological edge states for disordered bosonic systems
• Z2 phase diagram of three-dimensional disordered topological insulator via scattering matrix approach
• Bulk Spectrum and K-theory for Infinite-Area Topological Quasicrystal
• Effect of Strong Disorder on 3-Dimensional Chiral Topological Insulators: Phase Diagrams, Maps of the Bulk Invariant and Existence of Topological Extended Bulk States
• Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus
• Superuniversality of topological quantum phase transition and global phase diagram of dirty topological systems in three dimensions
• A New Numerical Method for ${\mathbb{Z}}_2$ Topological Insulators with Strong Disorder
• Topological Insulator in an Atomic Liquid
• Fractionalized topological insulators from frustrated spin models in three dimensions
• Local formula for the $Z_2$ invariant of topological insulators
• The tenfold way redux: Fermionic systems with $N$-body interactions

Cited by in corpus (21)

• Structural Disorder Induced Second-order Topological Insulators in Three Dimensions
• Topological Weaire-Thorpe models of amorphous matter
• Amorphous topological matter: theory and experiment
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Local Topological Markers in Odd Spatial Dimensions and Their Application to Amorphous Topological Matter
• Symmetry-Protected Topological Phases in a Rydberg Glass
• Fractionalization and topology in amorphous electronic solids
• Criticality in amorphous topological matter -- beyond the universal scaling paradigm
• Topological Random Fractals
• Structural and electronic properties of realistic two-dimensional amorphous topological insulators
• Amorphous Bi${}_2$Se${}_3$ structural, electronic, and topological nature by first-principles
• Noncrystalline topological superconductors
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Density-driven higher-order topological phase transitions in amorphous solids
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Topological diffusive metal in amorphous transition metal monosilicides
• Topological phases of amorphous matter
• Quantum Hall criticality in an amorphous Chern insulator
• Topological band insulators without translational symmetry
• Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals
• Non-self-averaging topological Anderson insulator