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

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 ofanomalous 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.