Topological Devil's staircase in atomic two-leg ladders

TL;DR

This paper demonstrates a hierarchy of topological phases called the topological Devil's staircase in interacting one-dimensional systems, revealing novel symmetry-protected topological density waves at fractional fillings.

Contribution

It introduces a new topological phase hierarchy in 1D interacting systems with fractional fillings, supported by field theory and numerical analysis, extending understanding beyond non-interacting models.

Findings

Identification of topological density waves at fractional fillings

Edge modes are gapped, breaking bulk-edge correspondence

Relevance to cold atom experiments with optical lattices

Abstract

We show that a hierarchy of topological phases in one dimension -- a topological Devil's staircase -- can emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes a topological or a crystalline topological insulator. Focusing on a specific example in the BDI class, we present a field-theoretical argument based on bosonization that indicates how the system, as a function of the filling fraction, hosts a series of density waves. Subsequently, based on a numerical investigation of the low-lying energy spectrum, Wilczek-Zee phases, and entanglement spectra, we show that they are symmetry protected topological phases. In sharp contrast to the non-interacting limit, these topological density waves do not follow the bulk-edge correspondence, as their edge modes are gapped. We then discuss how these results are immediately applicable to models in the AIII class, and to crystalline topological insulators protected by inversion symmetry. Our findings are immediately relevant to cold atom experiments with alkaline-earth atoms in optical lattices, where the band structure properties we exploit have been recently realized.