${}^3$He-R: A Topological $s^{\pm }$ Superfluid with Triplet Pairing

Abstract

We show that when spin and orbital angular momenta are entangled by spin-orbit coupling, this transforms a topological spin-triplet superfluid/superconductor state, such as ${}^3$He-B, into a topological $s^{\pm }$ state, with non-trivial gapless edge states. Similar to ${}^3$He-B, the $s^{\pm }$ state also minimizes on-site Coulomb repulsion for weak to moderate interactions. A topological phase transition into a $d$-wave state occurs for sufficiently strong spin-orbit coupling.

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• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Anomalous Andreev bound state in non-centrosymmetric superconductors