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

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.

13 pages, 12 figures

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Cited by in corpus (8)

• Dynamical quantum phase transitions in a mesoscopic superconducting system
• Multiterminal transport spectroscopy of subgap states in Coulomb-blockaded superconductors
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Transient effects in quantum dots contacted via topological superconductor
• Absence of thermalization of free systems coupled to gapped interacting reservoirs
• Phase transitions in quantum dot-Majorana zero mode coupling systems
• Quench dynamics of Fano-like resonances in the presence of the on-dot superconducting pairing
• Transient triplet blockade in Andreev junction