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.

arXiv comment13 pages, 12 figures

References in corpus (94)

• Kondo Physics in a Single Electron Transistor
• Real time evolution using the density matrix renormalization group
• Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications
• Time-evolution methods for matrix-product states
• Hamiltonian approach to the transport properties of superconducting quantum point contacts
• Revival of the Kondo effect
• From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires
• Supercurrent reversal in quantum dots
• AC JOSEPHSON EFFECT IN A SINGLE QUANTUM CHANNEL
• Quantum supercurrent transistors in carbon nanotubes
• Revealing the electronic structure of a carbon nanotube carrying a supercurrent
• Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
• Josephson and Andreev transport through quantum dots
• Coherent manipulation of Andreev states in superconducting atomic contacts
• High-resolution studies of the Majorana atomic chain platform
• Nonequilibrium electron transport using the density matrix renormalization group
• Josephson Current through a correlated quantum level: Andreev states and Pi-junction behavior
• Higgs Mode in Superconductors
• Kondo Effect and Josephson Current through a Quantum Dot between Two Superconductors
• Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
• Kinky Behavior in Josephson Junctions
• Twofold advance in the theoretical understanding of far-from-equilibrium properties of interacting nanostructures
• Resonant tunneling through a small quantum dot coupled to superconducting leads
• Critical Current 0-$\pi$ Transition in Designed Josephson Quantum Dot Junctions
• Ground State and Finite Temperature Lanczos Methods
• Josephson current through a single Anderson impurity coupled to BCS leads
• Josephson current through a nanoscale magnetic quantum dot
• Transport Through Andreev Bound States in a Graphene Quantum Dot
• Even-odd effect in Andreev Transport through a Carbon Nanotube Quantum Dot
• The Interacting Impurity Josephson Junction: Variational Wavefunctions and Slave Boson Mean Field Theory
• Tuning the Josephson current in carbon nanotubes with the Kondo effect
• Kondo effect in Normal-Superconductor Quantum Dots
• Loss of Pi-Junction Behaviour in an Interacting Impurity Josephson Junction
• Evidence for long-lived quasiparticles trapped in superconducting point contacts
• A finite-frequency functional RG approach to the single impurity Anderson model
• Tuning Yu-Shiba-Rusinov States in a Quantum Dot
• Andreev Bound States and Their Signatures
• Real-time diagrammatic approach to transport through interacting quantum dots with normal and superconducting leads
• Transport properties and Kondo correlations in nanostructures: the time-dependent DMRG method applied to quantum dots coupled to Wilson chains
• Non-equilibrium electronic transport in a one-dimensional Mott insulator
• Applying Adaptive Time-Dependent DMRG to Calculate the Conductance of Strongly Correlated Nanostructures
• Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction
• The Anderson-Josephson quantum dot -- A theory perspective
• Yu-Shiba-Rusinov screening of spins in double quantum dots
• Nonequilibrium dynamics in the one-dimensional Fermi-Hubbard model: A comparison of the nonequilibrium Green functions approach and the density matrix renormalization group method
• Kondo effect in asymmetric Josephson couplings through a quantum dot
• Multiple Andreev reflection in single atom niobium junctions
• Excitons in the One-Dimensional Hubbard Model: a Real-Time Study
• Understanding the Josephson current through a Kondo-correlated quantum dot
• Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model
• Time-dependent quantum transport with superconducting leads: a discrete basis Kohn-Sham formulation and propagation scheme
• Full-counting statistics of charge and spin transport in the transient regime: A nonequilibrium Green's function approach
• A weak coupling CTQMC study of the single impurity and periodic Anderson models with s-wave superconducting baths
• Dynamics of quasiparticle trapping in Andreev levels
• Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime
• Kondo resonance enhanced supercurrent in single wall carbon nanotube Josephson junctions
• Perturbation theory of a superconducting $0-\pi$ impurity quantum phase transition
• Waiting Time Distribution of Quantum Electronic Transport in Transient Regime
• Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads
• Non-equilibrium dynamics of Andreev states in the Kondo regime
• Nonequilibrium transport through a spinful quantum dot with superconducting leads
• Constructive influence of the induced electron pairing on the Kondo state
• The fate of the Kondo cloud in a superconductor
• Yu-Shiba-Rusinov qubit
• Unveiling odd-frequency pairing around a magnetic impurity in a superconductor
• The Andreev states of a superconducting quantum dot: mean field vs exact numerical results
• Quench dynamics in superconducting nanojunctions: metastability and dynamical Yang-Lee zeros
• Equilibrium and time-dependent Josephson current in one-dimensional superconducting junctions
• Interplay Between Yu-Shiba-Rusinov States and Multiple Andreev Reflections
• Andreev bound states formation and quasiparticle trapping in quench dynamics revealed by time-dependent counting statistics
• 0-Pi quantum transition in a carbon nanotube Josephson junction: Universal phase dependence and orbital degeneracy
• Superconducting non-equilibrium transport through a weakly interacting quantum dot
• Non-equilibrium transport through a point contact in the $\nu =5/2$ non-Abelian quantum Hall state
• Odd-frequency superconductivity near a magnetic impurity in a conventional superconductor
• Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads
• Real-time dynamics of particle-hole excitations in Mott insulator-metal junctions
• Dynamics of hybrid junctions of Majorana wires
• Spintronics meets density matrix renormalization group: Quantum spin torque driven nonclassical magnetization reversal and dynamical buildup of long-range entanglement
• Washing out of the 0-pi transition in Josephson junctions
• How long does it take to form the Andreev quasiparticles ?
• Photoexcitation of electronic instabilities in one-dimensional charge-transfer systems
• Time-dependent Andreev bound states of a quantum dot coupled to two superconducting leads
• Time scales for charge-transfer based operations on Majorana systems
• Transient dynamics in interacting nanojunctions within self-consistent perturbation theory
• Quench dynamics and relaxation of a spin coupled to interacting leads
• Quantum spin torque driven transmutation of antiferromagnetic Mott insulator
• Quench dynamics of correlated quantum dot proximitized to superconducting lead
• Higgs-like pair amplitude dynamics in superconductor-quantum dot hybrids
• Transient effects in double quantum dot sandwiched laterally between superconducting and metallic leads
• Cooper-pair transport through a Hubbard chain sandwiched between two superconductors: Density matrix renormalization group calculations
• Electron correlation effects in superconducting nanowires in and out of equilibrium
• Build-up of Vibron-Mediated Electron Correlations in Molecular Junctions
• Time-dependent Andreev reflection
• Footprints of impurity quantum phase transitions in quantum Monte Carlo statistics

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