Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry

TL;DR

This paper demonstrates that the gapless boundary modes of 3D higher-order topological insulators and superconductors with inversion symmetry can be gapped by introducing non-Abelian surface topological order, revealing an anomalous boundary phenomenon.

Contribution

It introduces the concept of anomalous gapped boundaries between topological orders in higher-order topological phases with inversion symmetry, highlighting a new interacting manifestation of higher-order topology.

Findings

Gapless boundary modes can be gapped without symmetry breaking.

Surface topological order exhibits anomalous fractionalization patterns.

Boundary phenomena are consistent only on the surface of a 3D higher-order topological phase.

Abstract

We show that the gapless boundary signatures - namely, chiral/helical hinge modes or localized zero modes - of three-dimensional higher-order topological insulators and superconductors with inversion symmetry can be gapped without symmetry breaking upon the introduction of non-Abelian surface topological order. In each case, the fractionalization pattern that appears on surface is `anomalous' in the sense that it can be made consistent with symmetry only on the surface of a three dimensional higher-order insulator/superconductor. Our results show that the interacting manifestation of higher-order topology is the appearance of `anomalous gapped boundaries' between distinct topological orders whose quasiparticles are related by inversion, possibly in conjunction with other protecting symmetries such as TRS and charge conservation.