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arXiv:2108.05959 · Physical review. B./Physical review. B

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

Rubén Seoane Souto, Adrian E. Feiguin, A. Martín‐Rodero, A. Levy Yeyati

Published Dec 16, 2021• 10 citations
arXivHTMLPDF

Abstract

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 ($0\text{\ensuremath{-}}\ensuremath{\pi}$ 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 $\ensuremath{\pi}$ 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.

DOI
10.1103/physrevb.104.214506

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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\ensuremath-\ensuremathπ0\text{\ensuremath{-}}\ensuremath{\pi}0\ensuremath-\ensuremathπ 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 \ensuremathπ\ensuremath{\pi}\ensuremathπ 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.
We study the non-equilibrium dynamics of a spinful single-orbital quantum dot with an incorporated quantum mechanical spin-1/2 magnetic impurity. Due to the spin degeneracy, double occupancy is allowed, and Coulomb interaction together with the exchange coupling of the magnetic impurity influence the dynamics. By extending the iterative summation of real-time path integrals (ISPI) to this coupled system, we monitor the time-dependent non-equilibrium current and the impurity spin polarization to determine features of the time-dependent non-equilibrium dynamics. We particulary focus on the deep quantum regime, where all time and energy scales are of the same order of magnitude and no small parameter is available. We observe a significant influence of the non-equilibrium decay of the impurity spin polarization both in the presence and in the absence of Coulomb interaction. The exponential relaxation is faster for larger bias voltages, electron–impurity interactions and temperatures. We show that the exact relaxation rate deviates from the corresponding perturbative result. In addition, we study in detail the impurity's back action on the charge current and find a reduction of the stationary current for increasing coupling to the impurity. Moreover, our approach allows us to systematically distinguish mean-field Coulomb and impurity effects from the influence of quantum fluctuations and flip-flop scattering, respectively. In fact, we find a local maximum of the current for a finite Coulomb interaction due to the presence of the impurity.
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