Josephson currents in chaotic quantum dots

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 σ-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. arXiv:1804.02782v2 [cond-mat.supr-con] 30 May 2018

Topological supercurrents interaction and fluctuations in the multiterminal Josephson effect

“…This is the circular ensemble, introduced by Dyson, and shown to apply to a chaotic cavity by Blumel and Smilansky [49]. In other words we consider a SNS junction where the normal region is a chaotic quantum dot [50].…”

Peculiarities of the density of states in SN bilayers

“…Our results demonstrate that behavior of the DoS near E = ∆ 0 is very sensitive to the boundary conditions, and the full check-mark behavior can be easily destroyed (e.g., by finite κ). At the same time, it has been recently shown that the SN interface in the form of constriction (quantum point contact) can stabilize this type of peculiarity stretching it into a secondary gap ("smile" gap) in the DoS [26][27][28][29]. These results were obtained in setups with the N part represented by a chaotic cavity (quantum dot), implying the Green functions constant in space (0D limit).…”

Mesoscopic fluctuations in superconductor-topological insulator Josephson junctions

“…It should be stressed that the sub-and above the gap features in the DoS are extremely sensitive to the boundary action used in the saddle point analysis of Usadel equation. For instance, in the model of transparent interfaces, that can be captured by the full circuit-theory action [55], the DoS in the sub-gap region may display secondary gaps [25,26,30], while a singularity at ∆ may be turned into a vanishing DoS and an unusual structure of the crossover to higher energies arises [24].…”

“…[28] for the distribution of the minigap edge in the opposite limit E Th ≪ ∆. However, the implication of these interesting features on the supercurrent fluctuations has not been addressed, only an average current-phase relation was calculated [29,30]. Furthermore, Josephson junctions are typically operated in an external magnetic field, which introduces yet another energy scale E Φ into the problem.…”