Quartets and the Current-Phase Structure of a Double Quantum Dot Superconducting Bijunction at Equilibrium

TL;DR

This paper investigates the equilibrium current-phase relationship in a three-terminal superconducting bijunction with two quantum dots, revealing nonlocal effects and degeneracies influenced by interdot couplings and temperature.

Contribution

It provides a detailed analysis of nonlocal processes and degeneracies in a double quantum dot superconducting bijunction at equilibrium, highlighting the role of interdot coupling.

Findings

Degenerate midgap Andreev states can appear symmetrically.

Interdot coupling lifts degeneracy, inducing non-local inductance.

Nonlocal processes involve quartet tunneling and pair cotunneling.

Abstract

The equilibrium current-phase structure of a tri-terminal superconducting Josephson junction (bijunction) is analyzed as a function of the two relevant phases. The bijunction is made of two noninteracting quantum dots, each one carrying a single level. Nonlocal processes coupling the three terminals are described in terms of quartet tunneling and pair cotunneling. These couplings are due to nonlocal Andreev and cotunneling processes through the central superconductor $S_0$, as well as direct interdot coupling. In some cases, two degenerate midgap Andreev states appear, symmetric with respect to the ($\pi,\pi$) point. The lifting of this degeneracy by interdot couplings induces a strong non-local inductance at low enough temperatures. This effect is compared to the mutual inductance of a two-loop circuit.