Transient dynamics of a magnetic impurity coupled to superconducting electrodes: exact numerics versus perturbation theory

TL;DR

This paper investigates the transient behavior of a magnetic impurity in superconducting junctions using exact numerics and perturbation theory, revealing metastable states and relaxation mechanisms affecting supercurrent and impurity spin dynamics.

Contribution

It provides a comparative analysis of exact time-dependent density matrix renormalization group simulations and perturbative methods for impurity-superconductor systems, highlighting their agreement and physical insights.

Findings

Metastable states trap supercurrent below equilibrium levels.

Local Coulomb interactions do not relax trapped quasiparticles.

Coupling to a normal lead facilitates impurity spin relaxation.

Abstract

Impurities coupled to superconductors offer a controlled platform to understand the interplay between superconductivity, many-body interactions, and non-equilibrium physics. In the equilibrium situation, local interactions at the impurity induce a transition between the spin-singlet to the spin-doublet ground state, resulting in a supercurrent sign reversal ($0-\pi$ transition). In this work, we apply the exact time-dependent density matrix renormalization group method to simulate the transient dynamics of such superconducting systems. We also use a perturbative approximation to analyze their properties at longer times. These two methods agree for a wide range of parameters. In a phase-biased situation, the system gets trapped in a metastable state characterized by a lower supercurrent compared to the equilibrium case. We show that local Coulomb interactions do not provide an effective relaxation mechanism for the initially trapped quasiparticles. In contrast, other relaxation mechanisms, such as coupling to a third normal lead, make the impurity spin relax for parameter values corresponding to the equilibrium $0$ phase. For parameters corresponding to the equilibrium $\pi$ phase the impurity converges to a spin-polarized stationary state. Similar qualitative behavior is found for a voltage-biased junction, which provides an effective relaxation mechanism for the trapped quasiparticles in the junction.