${\mathbb{Z}}_2$ Topologically Obstructed Superconducting Order

Abstract

We propose a class of topological superconductivity in which the pairing order is ${\mathbb{Z}}_2$ topologically obstructed in a three-dimensional time-reversal invariant system. When two Fermi surfaces are related by time-reversal and mirror symmetries, such as those in a ${\mathbb{Z}}_2$ Dirac semimetal, the inter-Fermi-surface pairing in the weak-coupling regime inherits the band topological obstruction. As a result, the pairing order cannot be well-defined over the entire Fermi surface and forms a time-reversal invariant generalization of U($1$) monopole harmonic pairing. A tight-binding model of the ${\mathbb{Z}}_2$ topologically obstructed superconductor is constructed based on a doped ${\mathbb{Z}}_2$ Dirac semimetal and exhibits nodal pairings. At an open boundary, the system exhibits a time-reversal pair of topologically protected surface states.

8 pages, 6 figures

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