Odd-frequency pairing and Ising spin susceptibility in time-reversal invariant superfluids and superconductors

TL;DR

This paper explores how odd-frequency spin-triplet pairs in time-reversal invariant superfluids and superconductors influence surface magnetic responses, revealing symmetry constraints that lead to Ising-like anisotropy and potential susceptibility enhancements.

Contribution

It clarifies the role of discrete symmetries in constraining odd-frequency pair amplitudes and their impact on surface spin susceptibility in TRI superfluids and superconductors.

Findings

Surface OTE pairs exhibit Ising-like anisotropy due to symmetry constraints.

Breaking discrete symmetries enables OTE pairs to couple with external magnetic fields.

Surface spin susceptibility can be anomalously enhanced when symmetry is broken.

Abstract

We here examine the relation between odd-frequency spin-triple even-parity (OTE) Cooper pairs and anomalous surface magnetic response in time-reversal invariant (TRI) spin-triplet superfluids and superconductors. The spin susceptibility generally consists of two contributions: Even-frequency odd-parity pair amplitudes and odd-frequency even-parity pair amplitudes. The OTE pair amplitudes are absent in the bulk region, but ubiquitously exist in the surface and interface region as Andreev bound states. We here clarify that additional discrete symmetries, originating from the internal symmetry and point group symmetry, impose strong constraint on the OTE pair amplitudes emergent in the surface of TRI superfluids and superconductors. As a result of the symmetry constraint, the magnetic response of the OTE pairs yields Ising-like anisotropy. For the topological phase of the $^3$He-B in a restricted geometry, the coupling of the OTE pair amplitudes to an applied field is prohibited by an additional discrete symmetry. Once the discrete symmetry is broken, however, the OTE pairs start to couple to the applied field, which anomalously enhances surface spin susceptibility. Furthermore, we extend this theory to TRI superconductors, where the corresponding discrete symmetry is the mirror reflection symmetry.