Wannier band transitions in disordered π-flux ladders

摘要

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 of disorder, the topology of a disordered Wannier band, and disorder-induced Wannier transitions have not been extensively studied. In this Rapid Communication, we focus on the simplest example of a Wannier topological insulator: a mirror-symmetric π-flux ladder in one dimension. We find that the Wannier topology is robust to disorder, and derive a real-space renormalization group procedure to understand a different type of strong disorder-induced transition between nontrivial 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 still needs to be studied in the presence of disorder.