Josephson effect in two-band superconductors

Physical Review B: Condensed Matter and Materials Physics. 2020. Vol. 101. No. 184501. P. 184501-1–184501-6.

Sasaki A., Ikegaya S., Habe T., A.A. Golubov, Asano Y.

We study theoretically 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 ϕ1 and that at the second band ϕ2 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 δϕ1,
the phase difference at the second band δϕ2, and the difference at the center-of-mass phase (δϕ1 + δϕ2 )/2. A
Cooper pair generated by the band hybridization carries the last current component. We discuss the relation
between the Josephson current calculated in theories and that observed in experiments.

Keywords: эффект Джозефсона, сверхпроводники, Josephson effect, superconductors