Time-dependent Andreev bound states of a quantum dot coupled to two superconducting leads

Abstract

Sub-gap transport properties of a quantum dot (QD) coupled to two superconducting and one metallic leads are studied theoretically, solving the time-dependent equation of motion by the Laplace transform technique. We focus on time-dependent response of the system induced by a sudden switching on the QD-leads couplings, studying the influence of initial conditions on the transient currents and the differential conductance. We derive analytical expressions for measurable quantities and find that they oscillate in time with the frequency governed by the QD-superconducting lead coupling and acquire damping, due to relaxation driven by the normal lead. Period of these oscillations increases with the superconducting phase difference $\varphi$. In particular, for $\varphi =\pi$ the QD occupancy and the normal current evolve monotonically (without any oscillations) to their stationary values. In such case the induced electron pairing vanishes and the superconducting current is completely blocked. We also analyze time-dependent development of the Andreev bound states. We show, that the measurable conductance peaks do not appear immediately after sudden switching of the QD coupling to external leads but it takes some finite time-interval for the system needs create these Andreev states. Such time-delay is mainly controlled by the QD-normal lead coupling.

17 pages, 12 figures

References in corpus (31)

• Spectral properties of locally correlated electrons in a BCS superconductor
• Even-odd effect in Andreev Transport through a Carbon Nanotube Quantum Dot
• Transient dynamics of the Anderson impurity model out of equilibrium
• Real-time diagrammatic approach to transport through interacting quantum dots with normal and superconducting leads
• Charge transfer statistics of a molecular quantum dot with a vibrational degree of freedom
• The Anderson-Josephson quantum dot -- A theory perspective
• Full-counting statistics of charge and spin transport in the transient regime: A nonequilibrium Green's function approach
• Manipulating the magnetic state of a carbon nanotube Josephson junction using the superconducting phase
• Transient regime in non-linear transport through many-level quantum dots
• Time-Dependent Transport Through Molecular Junctions
• Spin-flip scattering in time-dependent transport through a quantum dot: Enhanced spin-current and inverse tunneling magnetoresistance
• Long transient dynamics in the Anderson-Holstein model out of equilibrium
• Systematic Perturbation Theory for Dynamical Coarse-Graining
• Ballistic supercurrent discretization and micrometer-long Josephson coupling in germanium
• Superconducting proximity effect and zero-bias anomaly in transport through quantum dots weakly attached to ferromagnetic leads
• Quench dynamics in superconducting nanojunctions: metastability and dynamical Yang-Lee zeros
• Spin-Dependent Ringing and Beats in a Quantum Dot System
• Time-dependent Landauer-Büttiker formula for transient dynamics
• Josephson-phase-controlled interplay between correlation effects and electron pairing in a three-terminal nanostructure
• Transient dynamics of the nonequilibrium Majorana resonant level model
• Time-dependent resonant tunneling transport: Keldysh and Kadanoff-Baym nonequilibrium Green's functions in an analytically soluble problem
• Time-dependent transport in open systems based on quantum master equations
• Renormalization effects in interacting quantum dots coupled to superconducting leads
• Quantum Monte Carlo study of nonequilibrium transport through a quantum dot coupled to normal and superconducting leads
• Ultrafast manipulation of electron spins in a double quantum dot device: A real-time view
• Transient dynamics in interacting nanojunctions within self-consistent perturbation theory
• Electron waiting times in hybrid junctions with topological superconductors
• Transient noise spectra in resonant tunneling setups: Exactly solvable models
• A partition-free approach to transient and steady-state charge currents
• Time-dependent quantum transport through an interacting quantum dot beyond sequential tunneling: second-order quantum rate equations
• Transient spin current under a thermal switch

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• Transient dynamics of a magnetic impurity coupled to superconducting electrodes: exact numerics versus perturbation theory
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• Subgap dynamics of double quantum dot coupled between superconducting and normal leads
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• Metastability and quantum coherence-assisted sensing in interacting parallel quantum dots