Triplet Superconductivity in a Nutshell

Abstract

The triplet superconductors have been around us since 1980, when Jerome et al. discovered the Bechgaard salts (TMTSF) 2 PF 6 and (TMTSF) 2 ClO 4 . Now there are more than 20 or so triplet superconductors discovered. Recently we found that most of them with the known gap symmetries can be mapped to the superfluid phase of 3 He-A and 3 He-A 1 . Further, in most of them,l (the chiral vector, i.e. the quantization axis of the pair angular momentum) is fixed parallel to one of the crystal axes and all the topological defects are considered in terms ofd-textures, wherê d is the spin vector. Then Sr 2 RuO 4 , UPt 3 , PrOs 4 Sb 12 and (TMTSF) 2 ClO 4 belong to type-A, which is an analog of superfluid 3 He-A. In these superconductors, a vortex splits into a pair of half quantum vortices (HQVs) at low temperatures. On the other hand, CePt 3 Si, CeIrSi 3 , CeRhSi 3 , UIr and Li 2 Pt 3 B (those in non-centrosymmetric crystals) belong to type-A 1 , which is an analog of superfluid 3 He-A 1 . In all of these triplet superconductors, vortices harbor the zero mode or the Majorana fermions, the implications of which deserves further exploration.

New Paradigm of Triplet Superconductivity

“…This makes the triplet superconductor with the admixture of the singlet superconductor (as proposed by Frigeri et al [11,12]) very unlikely. Recently (73) in [17] we have proposed that the triplet superconductors in non-centrosymmetric crystals should be like the one in 3 He-A 1 . The superconductivity occupies the Fermi surface associated with one spin component (say spin up) while the other Fermi surface remains in the normal state.…”

Pairing symmetries in the Zeeman-coupled extended attractive Hubbard model

“…On the contrary, the general consensus about the novel high cuprate superconductors is that they are identified as strong candidates for unconventional d -wave superconductors 9 – 11 , which support the formation of spin-singlet Cooper pairs with an anisotropic d -wave orbital OP symmetry. In general, Cooper pairs can also be formed in the spin-triplet state, with total spin and anisotropic orbital OP 12 , 13 . Recent studies revealed that a two dimensional chiral p -wave spin-triplet superconductor is a candidate to host Majorana fermions 14 – 16 .…”