Kondo effect in asymmetric Josephson couplings through a quantum dot

TL;DR

This study investigates how asymmetry in Josephson couplings through a quantum dot influences the ground state and phase transitions, revealing that coupling asymmetry stabilizes the singlet state and affects screening.

Contribution

It provides a detailed analysis of the impact of asymmetric couplings on the quantum phase transition in a superconducting quantum dot system using NRG.

Findings

Asymmetry stabilizes the singlet ground state.

Coupling asymmetry affects local moment screening.

Phase difference and gap size influence screening and ground state.

Abstract

Asymmetry in the Josephson couplings between two superconductors through a quantum dot is studied based on a single impurity Anderson model using the numerical renormalization group (NRG). Specifically, we examine how the difference between the couplings \Gamma_L and \Gamma_R affects the ground state, which is known to show a quantum phase transition between a nonmagnetic singlet and a magnetic doublet depending on the various parameters; the Coulomb interaction U, onsite potential \epsilon_d, level width \Gamma_L, \Gamma_R, caused by the hybridization, and superconducting gaps \Delta_L and \Delta_R for the leads on the left and right. Our results show that whether the local moment is fully screened or not depends substantially on the asymmetry in the couplings \Gamma_L \neq \Gamma_R. It tends to make the singlet ground state stable, while the size and phase difference of the two superconducting gaps tend to suppress the screening. We also discuss some general symmetry properties of the system and their relation to the current conservation.