Josephson Effect of two-band/orbital superconductors

Yasuhiro Asano

We have been interested in physics of an odd-frequency Cooper pair. At this conference, we will discuss two phenomena of two-band (two-orbital) superconductors. At first, we discuss the Josephson effect between two two-band superconductors respecting time-reversal symmetry, where we assume a spin-singlet s-wave pair potential in each conduction band. The superconducting phase at the first band ! and that at the second band " characterize a two-band superconducting state. We consider a Josephson junction where an insulating barrier separates two such two-band superconductors. By applying the tunnel Hamiltonian description, the Josephson current is calculated in terms of the anomalous Green’s function on either side of the junction. We find that the Josephson current consists of three components which depend on three types of phase differences across the junction: the phase difference at the first band !, the phase difference at the second band ", and the difference at the center-of-mass phase (! +")/2. A Cooper pair generated by the band hybridization carries the last current component.[1] Secondly, we also discuss the effects of random nonmagnetic impurities on superconducting transition temperature in a Cu doped Bi2Se3, for which four types of pair potentials have been proposed. Although all the candidates belong to s-wave symmetry, two orbital degrees of freedom in electronic structures enrich the symmetry variety of a Cooper pair such as even-orbital-parity and odd-orbital-parity. We consider realistic electronic structures of Cu-doped Bi2Se3 by using a tight-binding Hamiltonian on a hexagonal lattice and consider effects of impurity scatterings through the self-energy of the Green’s function within the Born approximation. We find that even-orbital-parity spin-singlet superconductivity is basically robust even in the presence of impurities. The degree of the robustness depends on the electronic structures in the normal state and on the pairing symmetry in orbital space. On the other hand, two odd-orbital-parity spin- triplet order parameters are always fragile in the presence of potential disorder. We also discuss relations between our conclusions and the results of another theoretical studies on the same issue.

[1] A. Sasaki, S. Ikegaya, T. Habe, A. A. Golubov, and YA, Phys Rev. B 101, 184501 (2020)
[2] T. Sato and YA, Phys Rev. B 102, 024516 (2020)