An anomalous higher-order topological insulator

TL;DR

This paper introduces an anomalous higher-order topological insulator (HOTI) phase that exhibits fractional corner charges and a quantized bulk quadrupole moment despite having a trivial nested Wilson loop invariant, expanding the understanding of topological phases.

Contribution

The authors demonstrate the existence of anomalous HOTI phases with non-trivial topology not captured by traditional invariants, and develop a new invariant to characterize these phases.

Findings

Anomalous HOTI phase with fractional corner charges.

Existence of topologically non-trivial phases with trivial nested Wilson loop.

Development of a new topological invariant for anomalous HOTIs.

Abstract

Topological multipole insulators are a class of higher order topological insulators (HOTI) in which robust fractional corner charges appear due to a quantized electric multipole moment of the bulk. This bulk-corner correspondence has been expressed in terms of a topological invariant computed using the eigenstates of the Wilson loop operator, a so called "nested Wilson loop" procedure. We show that, similar to the unitary Floquet operator describing periodically driven systems, the unitary Wilson loop operator can realize "anomalous" phases, that are topologically non-trivial despite having a trivial topological invariant. We introduce a concrete example of an anomalous HOTI, which has a quantized bulk quadrupole moment and fractional corner charges, but a vanishing nested Wilson loop index. A new invariant able to capture the topology of this phase is then constructed. Our work shows that anomalous topological phases, previously thought to be unique to periodically driven systems, can occur and be used to understand purely time-independent HOTIs.