Real-time diagrammatic approach to transport through interacting quantum dots with normal and superconducting leads

TL;DR

This paper develops a real-time diagrammatic theory to analyze transport phenomena in quantum dots connected to normal and superconducting leads, capturing equilibrium and non-equilibrium effects including Andreev and Josephson currents.

Contribution

It introduces a novel theoretical framework for quantum dot transport that accounts for both equilibrium and non-equilibrium superconducting proximity effects.

Findings

Calculation of Josephson and Andreev currents in a three-terminal setup.

Identification of 0- and π-state transitions as functions of gate and bias voltages.

Description of Andreev bound states formation in the large-gap limit.

Abstract

We present a real-time diagrammatic theory for transport through interacting quantum dots tunnel coupled to normal and superconducting leads. Our formulation describes both the equilibrium and non-equilibrium superconducting proximity effect in a quantum dot. We study a three-terminal transistor geometry, consisting of a single-level quantum dot tunnel coupled to two phase-biased superconducting leads and one voltage-biased normal lead. We compute both the Josephson current between the two superconductors and the Andreev current in the normal lead, and analyze their switching on and off as well as transitions between 0- and $\pi$-states as a function of gate and bias voltage. For the limit of large superconducting gaps in the leads, we describe the formation of Andreev bound states within an exact resummation of all orders in the tunnel coupling to the superconducting leads, and discuss their signature in the non-equilibrium Josephson- and Andreev- current and the quantum-dot charge.