Topological Hopf-Chern Insulators and the Hopf Superconductor

TL;DR

This paper introduces new three-dimensional topological phases, including Hopf-Chern insulators and the Hopf superconductor, characterized by novel topological invariants and confirmed by the presence of gapless surface modes.

Contribution

It presents the construction of new topological phases using the Pontryagin-Thom method, expanding the classification of topological insulators and superconductors in three dimensions.

Findings

Discovery of infinitely many Hopf-Chern topological insulators.

Identification of a $\

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Abstract

We introduce new three-dimensional topological phases of two-band models using the Pontryagin-Thom construction. In symmetry class A these are the infinitely many Hopf-Chern topological insulators, which are hybrids of layered Chern insulators and the Hopf insulator. In symmetry class C, there is a $\mathbb{Z}_2$-classification with the non-trivial topological phase, the Hopf superconductor, being realized by a construction that doubles the usual Hopf insulator in momentum space. For these new topological phases we investigate the energy spectrum in the presence of a boundary and find gapless surface modes, confirming the validity of the bulk-boundary correspondence.