Subgap states in superconducting islands

TL;DR

This paper investigates subgap states in a superconducting island coupled to a quantum dot, revealing how charging energy influences their stability and spectral properties, with implications for quantum device design.

Contribution

It introduces an efficient matrix-product-operator approach to study Coulomb interactions in superconducting islands and systematically analyzes the effects of charging energy on subgap states.

Findings

Subgap states are stabilized by Kondo exchange and Coulomb-driven charge redistribution.

Spectral peaks are asymmetric and can change discontinuously with gate voltages.

Distinct excitation spectra are observed for even and odd superconductor ground states.

Abstract

We study an interacting quantum dot in contact with a superconducting island described by the Richardson model with a Coulomb repulsion term controlling the number of electrons on the island. This Hamiltonian admits a compact matrix-product-operator representation and can be efficiently and accurately solved using the density-matrix renormalization group. We systematically explore the effects of the charging energy $E_c$. For $E_c$ comparable to the superconducting gap $\Delta$, the subgap states are stabilized by the combination of Kondo exchange coupling and charge redistribution driven by the Coulomb interaction. The subgap states exist for both even and odd superconductor ground-state occupancy, but with very distinctive excitation spectra in each case. The spectral peaks are not symmetric with respect to the chemical potential and may undergo discontinuous changes as a function of gate voltages.