The Bulk-Edge Correspondence for Disordered Chiral Chains

Abstract

We study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given Hamiltonian with nearest neighbor hopping the two indices are equal. We also give a new formulation of the index in terms of the Lyapunov exponents of the zero energy Schrödinger equation, which illustrates the conditions for a topological phase transition occurring in the mobility gap regime.

arXiv comment20 pages, 3 figures

References in corpus (12)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• The Non-Commutative Geometry of the Quantum Hall Effect
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Scattering formula for the topological quantum number of a disordered multi-mode wire
• Symmetry classes of disordered fermions
• Delocalization in coupled one-dimensional chains
• Equality of bulk and edge Hall conductance revisited
• Equality of the bulk and edge Hall conductances in a mobility gap
• The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors
• Fredholm Indices and the Phase Diagram of Quantum Hall Systems

Cited by in corpus (30)

• Anomalous bulk-edge correspondence in continuous media
• Real-space representation of winding number for one-dimensional chiral-symmetric topological insulator
• Topologically protected edge modes in one-dimensional chains of subwavelength resonators
• High-order topological insulators from high-dimensional Chern insulators
• Topological characterization of classical waves: the topological origin of magnetostatic surface spin waves
• Microlocal analysis of the bulk-edge correspondence
• Functional analytic methods for discrete approximations of subwavelength resonator systems
• Strongly Disordered Floquet Topological Systems
• Wave topology brought to the coast
• Estimating bulk and edge topological indices in finite open chiral chains
• The Bulk-Edge Correspondence in Three Simple Cases
• Rational Approximations of Quasi-Periodic Problems via Projected Green's Functions
• Characterization of edge states in perturbed honeycomb structures
• Localization via Quasi-Periodic Bulk-Bulk Correspondence
• Chiral Flow in One-dimensional Floquet Topological Insulators
• Topological states in disordered arrays of dielectric nanoparticles
• Majorana edge magnetization in the Kitaev honeycomb model
• Bulk-edge correspondence in two-dimensional topological semimetals: A transfer matrix study of antichiral edge modes
• Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher
• Fredholm Homotopies for Strongly-Disordered 2D Insulators
• Computing edge states without hard truncation
• Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory
• Is the continuum SSH model topological?
• Wave-packet propagation in a finite topological insulator and the spectral localizer index
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- part II: Higher-dimensional spectral invariants
• Boundary conditions and violations of bulk-edge correspondence in a hydrodynamic model
• A ${\mathbb{Z}}_2$ invariant for chiral and particle-hole symmetric topological chains
• Nonlinear edge modes from topological 1D lattices
• The curious spectra and dynamics of non-locally finite crystals