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.

5 pages, 4 Figures. 4 pages Supplement

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Cited by in corpus (5)

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• 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