Josephson currents in chaotic quantum dots

TL;DR

This paper theoretically investigates the Josephson current in chaotic quantum dots with ballistic contacts, revealing complex phase relationships, sub-gap states, and the influence of the Thouless energy on supercurrent harmonics.

Contribution

It introduces a detailed theoretical analysis of Josephson effects in chaotic quantum dots using nonlinear sigma-model Keldysh formalism, highlighting the role of Thouless energy and sub-gap states.

Findings

Supercurrent exhibits strongly anharmonic skewed phase dependence.

Second harmonic becomes comparable to the first when Thouless energy exceeds the superconducting gap.

Presence of sub-gap tail states and mesoscopic fluctuations in the quantum dot.

Abstract

We study theoretically the Josephson current-phase relationship in a chaotic quantum dot coupled to superconductors by ballistic contacts. In this regime, strong proximity effect induces superconductivity in the quantum dot that leads to a significant modification in the electron density of states and formation of multiple sub-gaps. The magnitude of the resulting supercurrent depends on the phase difference of the superconducting order parameter in the leads and shows strongly anharmonic skewed behavior. We find that when the Thouless energy on the dot exceeds the superconducting energy gap, the second harmonic of the supercurrent becomes comparable in magnitude to the first harmonic. To address these effects on the technical level, we use the nonlinear $\sigma$-model Keldysh formalism in the framework of the circuit theory to compute dependence of the density of states, Josephson energy, and current on the superconducting phases in the leads. We analyze how these quantities change as a function of the Thouless energy and the superconducting gap. Finally, we briefly discuss sub-gap tail states, mesoscopic supercurrent fluctuations, weak localization correction, and also touch on anharmonicity of gatemon qubits with quantum dot Josephson junctions.