# How long does it take to form the Andreev quasiparticles ?

## TL;DR

This paper investigates the transient dynamics of Andreev quasiparticle formation in a quantum dot system coupled to metallic and superconducting leads, providing analytic expressions for key time scales and effects of electron interactions.

## Contribution

It offers the first analytic derivation of time-dependent charge, pairing amplitude, and currents in a quantum dot with proximity-induced superconductivity, including interaction effects.

## Key findings

- Derived explicit formulas for charge occupancy and pairing amplitude over time.
- Identified the characteristic time scale for quasiparticle formation.
- Showed the interplay between Coulomb interactions and electron pairing effects.

## Abstract

We study transient effects in a setup, where the quantum dot (QD) is abruptly sandwiched between the metallic and superconducting leads. Focusing on the proximity-induced electron pairing, manifested by the in-gap bound states, we determine characteristic time-scale needed for these quasiparticles to develop. In particular, we derive analytic expressions for (i) charge occupancy of the QD, (ii) amplitude of the induced electron pairing, and (iii) the transient currents under equilibrium and nonequilibrium conditions. We also investigate the correlation effects within the Hartree-Fock-Bogolubov approximation, revealing a competition between the Coulomb interactions and electron pairing.