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

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.

arXiv comment16 pages, 6 figures

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• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Topology and symmetry of surface Majorana arcs in cyclic superconductors
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Majorana multipole response: General theory and application to wallpaper groups
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Influence of diffuse surface scattering on the stability of superconducting phases with spontaneous surface current generated by Andreev bound states
• Signatures of odd-frequency pairing in the Josephson junction current noise
• Anisotropic paramagnetic response of topological Majorana surface states in the superconductor ${\text{UTe}}_2$
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Majorana multipole response with magnetic point group symmetry
• Euler band topology in superfluids and superconductors
• Strong odd-frequency correlations in fully gapped Zeeman-split superconductors