The Role of Odd‐Frequency Pairing in Multiband Superconductors

Abstract

Recent progress in the understanding of multiband superconductivity and its relationship to odd‐frequency pairing are reviewed herein. The discussion begins by reviewing the emergence of odd‐frequency pairing in a simple two‐band model, providing a brief pedagogical overview of the formalism. Several examples of multiband superconducting systems are examined, in each case describing both the origin of the band degree of freedom and the nature of the odd‐frequency pairing. Throughout, it is attempted to convey a unified picture of how odd‐frequency pairing emerges in these materials and propose that similar mechanisms are responsible for odd‐frequency pairing in several analogous systems: layered 2D heterostructures, double quantum dots, double nanowires, Josephson junctions, and systems described by isolated valleys in momentum space. In addition, experimental probes of odd‐frequency pairing in multiband systems are reviewed, focusing on hybridization gaps in the electronic density of states, paramagnetic Meissner effect, and Kerr effect.

Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model

“…3(c). Therefore, we conclude that band hybridization gives rise to pseudogaps at higher energies in the DOS of the SC SSH model, which is also similar to what occurs in certain two-band superconductors [46][47][48][49].…”

“…Odd-ω pairing can also appear as a bulk effect in superconductors, without the need of interfaces. This occurs in systems with multiple degrees of freedom such as multiband superconductors [46][47][48][49], double quantum dots [50,51], and double nanowires [35,52], where the band, dot, or wire indices, respectively, allow for a more broadened family of Cooper pair symmetries where odd-ω correlations can then emerge without the need of interfaces as in junctions. In particular, in multiband superconductors it has been shown that odd-ω pairing can be correlated with observable signatures such as gaps in the density of states (DOS) at higher energies [47] and the Kerr effect [53,54].…”

Proximity-Induced Odd-Frequency Superconductivity in a Topological Insulator

“…The band inversion in Bi 2 Se 3 implies that the bulk conduction and valence bands are formed by two orbitals with different parity, originating from hybridized Se and Bi p z states. This orbital degree of freedom in the TI allows for the generation of odd-frequency pairing components, in addition to the even-frequency ones [47]. For a proximitycoupled TI to a singlet s-wave SC, the symmetry allowed odd-(even-) frequency components are odd (even) in the orbital index [38].…”

Thermoelectricity carried by proximity-induced odd-frequency pairing in ferromagnet/superconductor junctions

“…where ζ = diag (1, 1, −1, −1), to find the scattering coefficients of Eqs. (19) and (22). Note that the effect of the interfacial RSOI enters through the boundary condition [38].…”

“…This unusual pairing obeys some exotic symmetries, such as s-wave spin-triplet and p-wave spin-singlet symmetry [4]. It has mostly been found in hybrid structures like ferromagnet (FM)/superconductor (SC) [6][7][8][9][10][11], normal metal/SC [12][13][14][15], and multiband systems with inter-band hybridization [16][17][18][19].…”