Supercurrent through a serial quantum dot close to singlet-triplet degeneracy

TL;DR

This paper studies supercurrent behavior in a double quantum dot system near singlet-triplet degeneracy, revealing a discontinuous jump in supercurrent magnitude related to quantum state transitions, using advanced theoretical methods.

Contribution

It introduces a comprehensive analysis of supercurrent in serial quantum dots near singlet-triplet degeneracy, employing FRG and analytical methods to reveal a generic discontinuity in supercurrent.

Findings

Supercurrent exhibits a 0-pi transition near B~t.

Discontinuous jump in supercurrent magnitude at B=t.

Analytical results in the Delta=infty limit support the numerical findings.

Abstract

We investigate two serially-aligned quantum dots in the molecular regime of large tunnel couplings t. A Zeeman field B is used to tune the energy difference of singlet and triplet spin configurations. Attaching this geometry to BCS source and drain leads with gap Delta and phase difference phi gives rise to an equilibrium supercurrent J. To compute J in presence of Coulomb interactions U between the dot electrons, we employ the functional renormalization group (FRG). For B\simt -- where the singlet and lowest-lying triplet spin states are equal in energy -- the current exhibits characteristics of a 0-pi transition similar to a single impurity. Its magnitude in the pi phase, however, jumps discontinuously at B=t, being smaller on the triplet side. Exploiting the flexibility of the FRG, we demonstrate that this effect is generic and calculate J for realistic experimental parameters Delta, U, and gate voltages epsilon. To obtain a more thorough understanding of the discontinuity, we analytically treat the limit Delta=infty where one can access the exact many-particle states. Finally, carrying out perturbation theory in the dot-lead couplings substantiates the intuitive picture that Cooper pair tunneling is favored by a singlet spin configuration while inhibited by a triplet one.