# Quantum capacitance of a superconducting subgap state in an electrostatically floating dot-island

**Authors:** Filip K. Malinowski, R. K. Rupesh, Luka Pavešić, Zoltán Guba, Damaz de Jong, Lin Han, Christian G. Prosko, Michael Chan, Yu Liu, Peter Krogstrup, András Pályi, Rok Žitko, Jonne V. Koski  
**arXiv:** [2210.01519](https://arxiv.org/abs/2210.01519)  
**Date:** 2022-10-04  
**Summary page:** https://www.summarizepaper.com/en/paper/2210.01519v2/

## Key points

- Hybrid device: InAs nanowire with epitaxial Al shell containing a quantum dot in contact with a superconducting island
- Device designed to be electrically floating, allowing access to highly excited and unstable states
- Researchers use radio-frequency reflectometry with lumped-element resonators to investigate the properties of the system
- Specifically examine quantum-dot-induced subgap states controlled by tunnel coupling
- Thermal excitations strongly suppress capacitance loading the resonator, known as "thermal screening"
- Single-level Anderson impurity model successfully explains observed resonance frequency shifts and changes in quality factor during charge transitions
- Measurement method and analysis framework can be applied to more complex hybrid devices
- Provides insights into behavior of superconducting subgap states in electrostatically floating dot-island systems

## Summary

This study focuses on a hybrid device consisting of an InAs nanowire with an epitaxial Al shell that contains a quantum dot in contact with a superconducting island. The device is designed to be electrically floating, which prevents direct transport measurements but allows access to states that would otherwise be highly excited and unstable. To investigate the properties of this system, the researchers employ radio-frequency reflectometry with lumped-element resonators, which capacitively couple to the quantum dot and can detect discrete subgap states. In this work, the authors specifically examine the case where there are no island states present but instead focus on quantum-dot-induced subgap states controlled by tunnel coupling. They find that when the gap between these subgap states and the quasi-continuum of excited states is small, thermal excitations strongly suppress the capacitance loading the resonator. This effect, termed "thermal screening," leads to significant changes in resonance frequency shift and quality factor at charge transitions. To understand and explain their experimental results, the researchers utilize a single-level Anderson impurity model. This model successfully accounts for the observed resonance frequency shifts and changes in quality factor during charge transitions. The measurement method established in this study, as well as the analysis and simulation framework employed, can be applied to more complex hybrid devices such as Andreev molecules or Kitaev chains. Overall, this research provides valuable insights into the behavior of superconducting subgap states in electrostatically floating dot-island systems and lays a foundation for further investigations into related phenomena.