Phase-dependent magnetoconductance fluctuations in a chaotic Josephson junction

TL;DR

This paper develops a random-matrix theory to describe phase-dependent magnetoconductance fluctuations in chaotic Josephson junctions, explaining experimental observations of conductance behavior under different coupling regimes.

Contribution

It introduces an extended circular ensemble model to analyze how conductance fluctuations depend on magnetic field and phase difference in chaotic quantum dots.

Findings

Weak coupling yields harmonic phase dependence.

Strong coupling results in random 2π-periodic conductance.

Theory aligns with experimental and existing theoretical results.

Abstract

Motivated by recent experiments by Den Hartog et al., we present a random-matrix theory for the magnetoconductance fluctuations of a chaotic quantum dot which is coupled by point contacts to two superconductors and one or two normal metals. There are aperiodic conductance fluctuations as a function of the magnetic field through the quantum dot and $2\pi$-periodic fluctuations as a function of the phase difference $\phi$ of the superconductors. If the coupling to the superconductors is weak compared to the coupling to the normal metals, the $\phi$-dependence of the conductance is harmonic, as observed in the experiment. In the opposite regime, the conductance becomes a random $2\pi$-periodic function of $\phi$, in agreement with the theory of Altshuler and Spivak. The theoretical method employs an extension of the circular ensemble which can describe the magnetic field dependence of the scattering matrix.