Transient effects in double quantum dot sandwiched laterally between superconducting and metallic leads

TL;DR

This paper investigates the transient dynamics of a double quantum dot system coupled to superconducting and metallic leads, revealing how initial states and interactions influence the emergence of in-gap states and the proximity effect.

Contribution

It provides explicit time-dependent expressions for occupancies and currents, analyzes the impact of initial conditions and correlations, and proposes experimental detection methods for transient phenomena.

Findings

Initial occupancy affects in-gap state development.

Correlation effects modify quasiparticle behavior and transient times.

Dynamical Andreev blockade is prominent in weak inter-dot coupling.

Abstract

We study the transient phenomena appearing in a subgap region of the double quantum dot coupled in series between the superconducting and normal metallic leads, focusing on the development of the superconducting proximity effect. For the uncorrelated nanostructure we derive explicit expressions of the time-dependent occupancies in both quantum dots, charge currents, and electron pairing induced on individual dots and between them. We show that the initial configurations substantially affect the dynamical processes, in which the in-gap bound states emerge upon coupling the double quantum dot to superconducting reservoir. In particular, the superconducting proximity effect would be temporarily blocked whenever the quantum dots are initially singly occupied. Such {\it triplet}/{\it Andreev blockade} has been recently reported experimentally for double quantum dots embedded in the Josephson [D. Bouman et al., Phys. Rev. B 102, 220505 (2020)] and Andreev [P. Zhang et al., arXiv:2102.03283 (2021)] junctions. We also address the role of correlation effects within the lowest-order decoupling scheme and by the time-dependent numerical renormalization group calculations. Competition of the repulsive Coulomb interactions with the superconducting proximity effect leads to renormalization of the in-gap quasiparticles, speeding up the quantum oscillations and narrowing a region of transient phenomena, whereas the dynamical Andreev blockade is well pronounced in the weak inter-dot coupling limit. We propose feasible methods for detecting the characteristic time-scales that could be observable by the Andreev spectroscopy.