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

Impurities coupled to superconductors offer a controlled platform to understand the interplay between superconductivity, many-body interactions, and nonequilibrium physics. In the equilibrium situation, local interactions at the impurity induce a transition from the spin-singlet to the spin-doublet ground state, resulting in a supercurrent sign reversal (0-ir 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 ir 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.

Automated summary

Impurities coupled to superconductors provide a controlled platform to study the interplay of superconductivity, many-body interactions, and nonequilibrium physics. Local interactions at the impurity induce transitions in the ground state and affect supercurrent behavior. Different relaxation mechanisms influence the behavior of trapped quasiparticles in the system, with Coulomb interactions not being effective for relaxation in certain cases. Voltage-biased junctions provide an effective relaxation mechanism for trapped quasiparticles.