Symmetry analysis of odd- and even-frequency superconducting gap symmetries for time-reversal symmetric interactions

Abstract

Odd-frequency superconductivity describes a class of superconducting states where the superconducting gap is an odd function in relative time and Matsubara frequency. We present a group theoretical analysis based on the linearized gap equation in terms of Shubnikov groups of the second kind. By discussing systems with spin-orbit coupling and an interaction kernel which is symmetric under the reversal of relative time, we show that both even- and odd-frequency gaps are allowed to occur. Specific examples are discussed for the square lattice, the octahedral lattice, and the tetragonal lattice. For irreducible representations that are even under reversal of relative time the common combinations of $s$- and d-wave spin singlet and p-wave spin triplet gaps are revealed, irreducible representations that are odd under reversal of relative time give rise to $s$- and d-wave spin triplet and p-wave spin singlet gaps. Furthermore, we discuss the construction of a generalized Ginzburg-Landau theory in terms of the associated irreducible representations. The result complements the established classification of superconducting states of matter.

11 pages, 3 figures

References in corpus (3)

• Odd-frequency pairing in normal metal/superconductor junctions
• Signature of magnetic-dependent gapless odd frequency states at superconductor/ferromagnet interfaces
• Manifestation of the odd-frequency spin-triplet pairing state in diffusive ferromagnet / superconductor junctions

Cited by in corpus (4)

• Weak-Coupling Theory of Pair Density-Wave Instabilities in Transition Metal Dichalcogenides
• Superconductivity in Correlated Multi-Orbital Systems with Spin-Orbit Coupling: Coexistence of Even- and Odd-Frequency Pairing and the Case of Strontium Ruthenate
• Identifying Topological Superconductivity in 2D Transition-Metal Dichalcogenides
• Ferroelectricity-induced multiorbital odd-frequency superconductivity in SrTiO${}_3$