Self-consistent description of Andreev bound states in Josephson quantum dot devices

TL;DR

This paper presents a perturbative framework based on a superconducting atomic limit for accurately describing Andreev bound states in interacting quantum dots connected to superconducting leads, aiding interpretation of spectroscopic experiments.

Contribution

It introduces a self-consistent perturbative approach using an effective Hamiltonian to describe Andreev bound states in quantum dots with superconducting contacts, valid even for small gaps.

Findings

Accurate results compared to Numerical Renormalization Group calculations.

Applicable to interpreting experimental spectroscopic data.

Provides a natural starting point for analyzing proximity effects in quantum dots.

Abstract

We develop a general perturbative framework based on a superconducting atomic limit for the description of Andreev bound states (ABS) in interacting quantum dots connected to superconducting leads. A local effective Hamiltonian for dressed ABS, including both the atomic (or molecular) levels and the induced proximity effect on the dot is argued to be a natural starting point. A self-consistent expansion in single-particle tunneling events is shown to provide accurate results even in regimes where the superconducting gap is smaller than the atomic energies, as demonstrated by a comparison to recent Numerical Renormalization Group calculations. This simple formulation may have bearings for interpreting Andreev spectroscopic experiments in superconducting devices, such as STM measurements on carbon nanotubes, or radiative emission in optical quantum dots.