Anatomy of topological Anderson transitions
arXiv:2301.04565 · doi:10.1103/PhysRevB.108.224201
Abstract
We study mesoscopic signatures of the topological Anderson transitions in topological disordered chains. To this end we introduce an integer-valued sample-specific definition of the topological index in finite size systems. Its phase diagram exhibits a fascinating structure of intermittent topological phases, dubbed topological islands. Their existence is rooted in the real zeros of the underlying random polynomial. Their statistics exhibits finite-size scaling, pointing to the location of the bulk topological Anderson transition. While the average theories in AIII and BDI symmetry classes are rather similar, the corresponding patterns of topological islands and their statistics are qualitatively different. We also discuss observable signatures of sharp topological transitions in mesoscopic systems, such as persistent currents and entanglement spectra.
arXiv comment5 pages, 5 figures
References in corpus (49)
- Topological Insulators
- Topological insulators and superconductors
- Classification of topological quantum matter with symmetries
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Calculation of reduced density matrices from correlation functions
- Topological Anderson Insulator
- Theory of the topological Anderson insulator
- Observation of the topological Anderson insulator in disordered atomic wires
- Photonic Topological Anderson Insulators
- Quantized conductance at the Majorana phase transition in a disordered superconducting wire
- Numerical study of the topological Anderson insulator in HgTe/CdTe quantum wells
- Entanglement Spectrum of a Disordered Topological Chern Insulator
- Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
- Disorder-induced Floquet Topological Insulators
- The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
- Disordered Topological Insulators via -Algebras
- Aharonov-Bohm oscillations in disordered topological insulator nanowires
- Topological Anderson Insulator in Three Dimensions
- Scattering formula for the topological quantum number of a disordered multi-mode wire
- Disordered Topological Insulators: A Non-Commutative Geometry Perspective
- Topological Phase Transitions in Disordered Electric Quadrupole Insulators
- Non-Hermitian Topological Anderson Insulators
- Real-space calculation of the conductivity tensor for disordered topological matter
- Disordered weak and strong topological insulators
- Stabilizing topological phases in graphene via random adsorption
- Topological Anderson insulator phenomena
- Quantum criticality of quasi one-dimensional topological Anderson insulators
- The dependence of topological Anderson insulator on the type of disorder
- Higher-order Topological Anderson Insulators
- AIII and BDI Topological Systems at Strong Disorder
- Localization and Mobility Gap in Topological Anderson Insulator
- Topology vs. Anderson localization: non-perturbative solutions in one dimension
- Disorder-Induced Multiple Transition involving Z2 Topological Insulator
- Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
- Benefits of weak disorder in one dimensional topological superconductors
- Real space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems
- Localization, topology and quantized transport in disordered Floquet systems
- Disorder-induced topological phase transition in a 1D mechanical system
- Topological quantum number and critical exponent from conductance fluctuations at the quantum Hall plateau transition
- Disorder-induced Majorana zero modes in a dimerized Kitaev superconductor chain
- Persistent current and zero-energy Majorana modes in a p-wave disordered superconducting ring
- Persistent currents in Dirac fermion rings
- Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
- Disorder driven phase transitions in weak AIII topological insulators
- Weak quantization of non-interacting topological Anderson insulator
- Disorder-induced topology in quench dynamics
- Persistent current of relativistic electrons on a Dirac ring in presence of impurities
- Mesoscopic conductance fluctuations and noise in disordered Majorana wires