# Superconducting quantum dot and the sub-gap states

## TL;DR

This paper reviews the theoretical and experimental research on superconductor-quantum dot hybrid devices, focusing on sub-gap states and their impact on transport properties, with emphasis on Yu-Shiba-Rusinov states.

## Contribution

It provides a comprehensive overview of the current understanding of sub-gap states in superconductor-quantum dot systems, highlighting the use of numerical renormalization group methods.

## Key findings

- Sub-gap states significantly influence transport in superconductor-quantum dot devices.
- Numerical renormalization group accurately models Yu-Shiba-Rusinov states.
- Experimental and theoretical studies advance understanding of hybrid nanostructures.

## Abstract

Quantum dots are nanostructures made of semiconducting materials that are engineered to hold a small amount of electric charge (a few electrons) that is controlled by external gate and may hence be considered as tunable artificial atoms. A quantum dot may be contacted by conductive leads to become the active part of a single-electron transistor, a device that is highly conductive only at very specific gate voltages. In recent years a significant attention has been given to more complex hybrid devices, in particular superconductor-semiconductor heterostructures. Here I review the theoretical and experimental studies of small quantum-dot devices contacted by one or several superconducting leads. I focus on the research on the low-lying localized electronic excitations that exist inside the superconducting gap (Yu-Shiba-Rusinov states) and determine the transport properties of these devices. The sub-gap states can be accurately simulated using the numerical renormalization group technique, often providing full quantitative understanding of the observed phenomena.