Microwave response of an Andreev bound state

TL;DR

This paper develops a theoretical framework to analyze the microwave response of an Andreev bound state in a finite-length weak link, incorporating charging effects and Coulomb interactions.

Contribution

It introduces an effective low-energy Hamiltonian that captures Coulomb interactions and provides analytical response functions for the system.

Findings

Derived the linear response of current and charge to phase and gate voltages.

Provided an analytical form of the response functions in the low-frequency limit.

Presented a phenomenological model for weak links with finite length and charging effects.

Abstract

We develop a theory for the dynamics of an Andreev bound state hosted by a weak link of finite length for which charging effects are important. We derive the linear response of both the current through the link and charge accumulated in it with respect to the phase and gate voltage biases. The resulting matrix encapsulates the spectroscopic properties of a weak link embedded in a microwave resonator. In the low-frequency limit, we obtain the response functions analytically using an effective low-energy Hamiltonian, which we derive. This Hamiltonian minimally accounts for Coulomb interaction and is suitable for a phenomenological description of a weak link having a finite length.