Quench dynamics of Fano-like resonances in the presence of the on-dot superconducting pairing

TL;DR

This paper investigates the time evolution of Fano-like resonances in a double quantum dot system with superconducting pairing, focusing on how quickly these resonances form after abrupt changes in system parameters.

Contribution

It introduces a detailed analysis of quench dynamics in Fano-like resonances with superconducting pairing, highlighting the formation times and charge oscillations in such systems.

Findings

Resonance formation times depend on system parameters.

Charge oscillations reveal the dynamics of resonance stabilization.

Superconducting pairing influences the energy and time scales of resonance development.

Abstract

We explore the electron dynamics of a system composed of double quantum dot embedded between metallic and superconducting leads in a T-shape geometry. In nanoscopic systems, where electron transfer between electrodes can be realized via different paths, interference effects play an important role. For double quantum dot system in the chosen geometry, interference of electrons transferred between electrodes via the interfacial quantum dot and electrons scattered on the side dot gives rise to Fano-like interference. If such a system is additionally coupled to a superconducting electrode, together with the well-understood Fano resonance an additional resonance appears on the opposite side of the Fermi level. In the recent work [Sci. Rep. 10, 2881 (2020)], we showed that this resonance occurs solely as a result of the local pairing of non-scattered electrons with scattered ones. In this work, considering the quench dynamics, we explore how much time is required for formation of each of these resonances. In particular, (i) we analyze the charge oscillations between subsystems; (ii) we estimate the time required for each resonance to achieve stable equilibrium upon an abrupt change of interdot connection; (iii) we discuss a typical energy and time scales for experiments on similar architectures.