Wannier band transitions in disordered $\pi$-flux ladders

Abstract

Boundary obstructed topological insulators are an unusual class of higher-order topological insulators with topological characteristics determined by the so-called Wannier bands. Boundary obstructed phases can harbor hinge/corner modes, but these modes can often be destabilized by a phase transition on the boundary instead of the bulk. While there has been much work on the stability of topological insulators in the presence disorder, the topology of a disordered Wannier band, and disorder-induced Wannier transitions have not been extensively studied. In this work, we focus on the simplest example of a Wannier topological insulator: a mirror-symmetric $\pi$-flux ladder in 1D. We find that the Wannier topology is robust to disorder, and derive a real-space renormalization group procedure to understand a new type of strong disorder-induced transition between non-trivial and trivial Wannier topological phases. We also establish a connection between the Wannier topology of the ladder and the energy band topology of a related system with a physical boundary cut, something which has generally been conjectured for clean models, but has not been studied in the presence of disorder.

arXiv comment5 pages, 4 Figures. 4 pages Supplement

References in corpus (34)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Topological Crystalline Insulators in the SnTe Material Class
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topolectrical circuit realization of topological corner modes
• Observation of a phononic quadrupole topological insulator
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• The Quantum-Mechanical Position Operator in Extended Systems
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Topological classification of crystalline insulators through band structure combinatorics
• Inversion Symmetric Topological Insulators
• Electron Localization in the Insulating State
• Observation of the topological Anderson insulator in disordered atomic wires
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Edge modes in band topological insulators
• Statistical Topological Insulators
• A Computational Non-Commutative Geometry Program for Disordered Topological Insulators
• The non-commutative n-th Chern number
• Orbital polarization and magnetization for independent particles in disordered media
• Extended topological group structure due to average reflection symmetry
• Quantization of Topological Invariants under Symmetry-Breaking Disorder

Cited by in corpus (5)

• Realization of Surface-Obstructed Topological Insulators
• Unified characterization for higher-order topological phase transitions
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Proposal for realizing and probing topological crystalline insulators in optical lattices