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arXiv:cond-mat/0611134

Dynamic $0-π$ transition induced by pumping mechanism

Wen, Jun, Baigeng Wang, Qingyun Zhang, D. Y. Xing

Published Nov 6, 2006• 0 citations
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Abstract

Using Nambu$\otimes $spin space Keldysh Green's function approach, we present a nonequilibrium charge and spin pumping theory of a quantum dot in the mico-cavity coupled to two superconducting leads. It is found that the charge currents include two parts: The dissipationless supercurrent standing for the transfer of coherent Cooper pairs and the pumped quasi-particle current. The supercurrent exhibits a dynamic $0-π$ transition induced by the frequency and strength of the $σ_{-}$ polarized laser field. This dynamic transition is not affected by the strong Coulomb interaction. Especially, the spin current appears and is an even function of the phase difference between two superconductors when the frequency of the polarized laser field is larger than two times superconducting energy gap. Our theory serves as an extension to non-superconducting spintronics.

DOI
10.48550/arxiv.cond-mat/0611134

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Dynamic 0−π0-π0−π transition induced by pumping mechanism
Using Nambu⊗\otimes ⊗spin space Keldysh Green's function approach, we present a nonequilibrium charge and spin pumping theory of a quantum dot in the mico-cavity coupled to two superconducting leads. It is found that the charge currents include two parts: The dissipationless supercurrent standing for the transfer of coherent Cooper pairs and the pumped quasi-particle current. The supercurrent exhibits a dynamic 0−π0-π0−π transition induced by the frequency and strength of the σ−σ_{-}σ−​ polarized laser field. This dynamic transition is not affected by the strong Coulomb interaction. Especially, the spin current appears and is an even function of the phase difference between two superconductors when the frequency of the polarized laser field is larger than two times superconducting energy gap. Our theory serves as an extension to non-superconducting spintronics.
The combined action of a dc bias and a microwave drive on the transport characteristic of a superconductor-quantum dot-superconductor junction is investigated. To cope with time dependent nonequilibrium effects and interactions in the quantum dot, we develop a general formalism for the dynamics of the density operator based on a particle conserving approach to superconductivity. Without invoking a broken U(1) symmetry, we identify a dynamical phase connected to the coherent transfer of Cooper pairs across the junction. In the weak-coupling limit, we show that besides quasiparticle transport, proximity induced superconducting correlations manifest in anomalous pair tunneling involving the transfer of a Cooper pair. The resulting generalized master equation in presence of the microwave drive showcases the characteristic bichromatic response due to the combination of the ac Josephson effect and an ac voltage. Analytical expressions for all harmonics in the driving frequency of both the current and the reduced dot operator are given for arbitrary driving strength. For the net dc current, the resulting photon assisted processes give rise to rich current-voltage characteristics. In addition to photon assisted subgap transport, we find regions of total current inversion in the stability diagram. There, the junction acts as a pump with the net dc current flowing against the applied dc bias. The first harmonic of the current, being closely related to the nonlinear dynamic susceptibility of the junction, is discussed at finite applied dc bias.
The combined action of a DC bias and a microwave drive on the transport characteristic of a superconductor-quantum dot-superconductor junction is investigated. To cope with time dependent non-equilibrium effects and interactions in the quantum dot, we develop a general formalism for the dynamics of the density operator based on a particle conserving approach to superconductivity. Without invoking a broken U (1) symmetry, we identify a dynamical phase connected to the coherent transfer of Cooper pairs across the junction. In the weak coupling limit, we show that besides quasiparticle transport, proximity induced superconducting correlations manifest in anomalous pair tunneling involving the transfer of a Cooper pair. The resulting generalized master equation in presence of the microwave drive showcases the characteristic bichromatic response due to the combination of the AC Josephson effect and an AC voltage. Analytical expressions for all harmonics in the driving frequency of both the current and the reduced dot operator are given for arbitrary driving strength. For the net DC current the resulting photon assisted processes give rise to rich current-voltage characteristics. In addition to photon assisted subgap transport we find regions of total current inversion in the stability diagram. There, the junction acts as a pump with the net DC current flowing against the applied DC bias. The first harmonic of the current, being closely related to the nonlinear dynamic susceptibility of the junction, is discussed at finite applied DC bias.
The spin-pump effects caused by the rotating magnetic field on the supercurrent in a superconductor--quantum-dot--superconductor system are studied theoretically. By tuning the magnetic-field strength, the sign of the supercurrent can be changed from positive to negative, which results in the $\ensuremath{\pi}$-junction transition. The $\ensuremath{\pi}$-junction transition can also be tuned by the quantum dot energy level. The tunable $\ensuremath{\pi}$-junction transition is interpreted in the picture of the current carrying density of states, which clearly shows the enhancement, suppression, and reversion of the supercurrent.
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.
We investigate nonequilibrium transport through superconducting nanojunctions using a Liouville space approach. The formalism allows us to study finite-gap effects, and to account for both quasiparticle and Cooper-pair tunneling. With focus on the weak-tunneling limit, we study the stationary dc and ac current up to second order (cotunneling) in the hybridization energy. For the particular case of a strongly interacting quantum dot sandwiched between two superconductors, we identify the characteristic virtual processes that yield the Andreev and Josephson current and obtain the dependence on the gate and bias voltage for the dc current, the critical current, and the phase-dependent dissipative current. In particular, the critical current is characterized by regions in the stability diagram in which its sign changes from positive to negative, resulting in a multitude of $0\ensuremath{-}\ensuremath{\pi}$ transitions. The latter signal the interplay between strong interactions and tunneling at finite bias.
We report a first direct observation of proximity supercurrent in a single InAs self-assembled quantum dot coupled to superconducting electrodes. We utilize large SAQDs with strong dot-lead coupling allowing sufficient overlap of quantized state that charge fluctuation in the dot may exceed one electron. Although the charging energy is larger than the superconductivity gap, Δ, the voltage characteristic measured in the current-driven four-terminal geometry signifies a supercurrent flow though the dot. The observed critical current is of the order of 10 pA, and much smaller than expected from theory. This current also shows the parity effect with the number of electrons in the dot, suggesting that the singlet correlation impedes the Cooper pair tunneling.