Kondo effect in a hybrid superconductor–quantum-dot–superconductor junction with proximity-inducedp-wave pairing states

Abstract

We study the transport of a hybrid superconductor--quantum-dot--superconductor junction, dominated by the interplay between the Kondo effect and the proximity-induced $p$-wave pairing states. Each superconductor lead is fabricated with a semiconductor with Rashba spin-orbit coupling (RSOC) and the combination of an $s$-wave superconductor and a ferromagnet. The RSOC breaks the SU(2) spin-rotation symmetry and creates the spin-triplet pairing components under the proximity-induced superconducting pairing interaction. Different from the s-wave pairing case, the Kondo screening of the dot spin involves the orbital angular momentum conserved transitions between the $p$-wave pairing states. The Zeeman field inherent from the ferromagnet removes the spin degeneracy of the quasiparticles excited in the triplet states. As a result, the spin-induced Yu-Shiba-Rusinov (YSR) state exhibits Zeeman-dependent splitting behaviors, and the splitting of the YSR state leads to the 0-$\ensuremath{\pi}$ phase transition when the ground state is a Kondo singlet. The temperature-dependent magnetic susceptibility indicates that the dot spin should be partially screened due to the breaking of time-reversal symmetry.