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Physical Review B

Persistent current driven by the Josephson effect in a triple-quantum-dot ring with superconducting leads

Guang-Yu Yi, Zhichao Li, Xiaohui Chen, Haina Wu, Wei‐Jiang Gong

Published May 29, 2013• 14 citations
Publisher

Abstract

The Josephson effect in a superconductor/triple-quantum-dot ring/superconductor structure is theoretically investigated. We find that in this structure, interdot spin correlation can be driven, which contributes to the occurrence of new 0 and $\ensuremath{\pi}$ phases of the Josephson current. Moreover, in the 0-$\ensuremath{\pi}$ phase-transition process, an intermediate bistable phase appears in which the Josephson current is completely suppressed. By analyzing the interdot spin correlation, the electron motion mechanism is clarified. We then attribute the disappearance of the Josephson current to the occurrence of the Josephson-Fano effect. What is interesting is that the disappearing Josephson current is accompanied by the apparent persistent current in the ring whose direction is determined by the superconducting phase difference. With the calculated results, we consider such a structure to be a candidate for the realization of the persistent current bit.

DOI
10.1103/physrevb.87.195442

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The Josephson effect in a superconductor/triple-quantum-dot ring/superconductor structure is theoretically investigated. We find that in this structure, interdot spin correlation can be driven, which contributes to the occurrence of new 0 and \ensuremathπ\ensuremath{\pi}\ensuremathπ phases of the Josephson current. Moreover, in the 0-\ensuremathπ\ensuremath{\pi}\ensuremathπ phase-transition process, an intermediate bistable phase appears in which the Josephson current is completely suppressed. By analyzing the interdot spin correlation, the electron motion mechanism is clarified. We then attribute the disappearance of the Josephson current to the occurrence of the Josephson-Fano effect. What is interesting is that the disappearing Josephson current is accompanied by the apparent persistent current in the ring whose direction is determined by the superconducting phase difference. With the calculated results, we consider such a structure to be a candidate for the realization of the persistent current bit.
We investigate the influence of the Fano effect on the Josephson current through a quantum dot (QD) coupled to two identical superconductors (SCs). Our attention is focused on the situation where the Kondo spin singlet survives the superconductivity and the finite- U slave-boson mean-field method is adopted to treat the Kondo correlation. With the direct coupling between the two SCs increased, the Josephson current varies in different manners in different regimes. This is consistent with the variation of Josephson coupling, which exhibits characteristics similar to those shown by the conductance through a QD connected to normal leads. But unlike the normal conductance, a negative Josephson coupling region is formed in the dip of the characteristic asymmetric peak–dip structure. Accompanying this 0–π transition, a new kind of intermediate states is found, which are different from those caused by effective ferromagnetic interaction. This 0–π transition and the intermediate states are yielded entirely by the Fano effect.
We theoretically study the superconducting proximity effect in a quantum dot coupled to two superconducting leads when the intradot interaction between electrons is made attractive. Because of the superconducting proximity effect, the electronic states for the embedded quantum dot are either spin-polarized states with an odd occupation number or BCS-like states with an even occupation number. We show that in the presence of an external magnetic field, the system can exhibit quantum phase transitions of fermion parity associated with the occupation number. In this paper, we adopt a self-consistent theoretical method to extend our considerations beyond the so-called superconducting atomic limit in which the superconducting gap for the leads is assumed to be the largest energy scale. This method enables us to numerically investigate the electronic structure of the dot as a result of the attractive interaction. For energy phase diagrams in the regime away from the atomic limit, we find a reentrant behavior where a BCS-like phase of the dot exists in an intermediate range of the hybridization strength between the quantum dot and the leads. We also consider Josephson current-phase relations and identify a number of examples showing 0-$\ensuremath{\pi}$ phase transitions that may offer important switching effects.
We consider a quantum dot with intradot attractive interaction sandwiched between two superconducting leads. We show that the system possesses quantum phase transitions of fermion parity as long as an external magnetic field is present. Due to the superconducting proximity effects, the possible electronic states for the embedded quantum dot are spin-polarized states with odd occupation and BCS-like states with even occupation. In this work, we adopt a self-consistent theoretical method to extend our considerations beyond the superconducting atomic limit to numerically investigate implications of an attractive interaction in electronic structures. We discuss the difference between results obtained in and away from the atomic limit. We find a reentrant behavior in the energy phase diagram when Δ\DeltaΔ is an order of magnitude larger than the hybridization strength. We also consider the Josephson current phase relations and find a number of examples showing the 0−π0-\pi0−π phase transitions that may offer important switching effects.
Quantum devices and computers will need operational units in different architectural configurations for their functioning. The unit should be a simple "quantum toy," an easy to handle superposition state. Here such a novel unit of quantum mechanical flux state (or persistent current) in a conducting ring with three ferromagnetic quantum dots is presented. The state is labeled by the two directions of the persistent current, which is driven by the spin chirality of the dots, and is controlled by the spin (the spin Josephson effect). It is demonstrated that by the use of two connected rings, one can carry out unitary transformations on the input flux state by controlling one spin in one of the rings, enabling us to prepare superposition states. The flux is shown to be a quantum operation gate, and may be useful in quantum computing.
The case of a quantum dot connected to two superconducting leads is studied by using the narrow-band limit to describe the superconducting degrees of freedom. The model provides a simple theoretical framework, almost analytical, to analyze the interplay between the Kondo effect, superconductivity, and finite temperature. In the quantum dot Kondo regime, the model is completely characterized by the ratio $\ensuremath{\Delta}/J$, with $\ensuremath{\Delta}$ the superconducting gap and JJJ an effective antiferromagnetic exchange coupling between the dot and the leads. The model allows us to calculate, at any temperature TTT, the equilibrium Josephson current through the dot in a very straightforward way as a function of $\ensuremath{\Delta}/J$. The behavior of the current allows us to distinguish the four types of hybrid junctions: 0, ${0}^{\ensuremath{'}},{\ensuremath{\pi}}^{\ensuremath{'}}$, and $\ensuremath{\pi}$. The presence of the 0- and ${0}^{\ensuremath{'}}$-junction configurations are intrinsically linked to the Kondo effect in the quantum dot, while the $\ensuremath{\pi}$- and ${\ensuremath{\pi}}^{\ensuremath{'}}$-junction configurations are driven by the superconductivity in the leads. The Josephson critical current has a non-monotonic behavior with temperature, that may be used for the experimental characterization of the fundamental $0\ensuremath{-}\ensuremath{\pi}$ transition. The model allows us to obtain easily a phase diagram $\ensuremath{\Delta}/J$ vs temperature, from where we can obtain an overall picture on the stability of the different types of junctions. From the explicit analytical expressions for the ground-state, low-energy excitations, free energy, and Josephson current, it is easy to understand the physical nature of the main features of the critical current and the phase diagram. The results, obtained with a minimum of numerical effort, are in a good qualitative agreement with more demanding calculational approaches aimed to solve the full model.
Josephson junctions based on quantum dots offer a convenient tunability by means of local gates. Here we analyze a Josephson junction based on a serial double quantum dot in which the two dots are individually gated by phase-shifted microwave tones of equal frequency. We calculate the time-averaged current across the junction and determine how the phase shift between the drives modifies the current-phase relation of the junction. Breaking particle-hole symmetry on the dots is found to give rise to a finite average anomalous Josephson current with phase bias between the superconductors fixed to zero. This microwave gated weak link thus realizes a tunable ``Floquet ${\ensuremath{\varphi}}_{0}$ junction'' with maximum critical current achieved for driving frequencies slightly off resonance with the subgap excitation energy. We provide numerical results supported by an analytical analysis for infinite superconducting gap and weak interdot coupling. We identify an interaction-driven $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition of anomalous Josephson current as a function of driving phase difference. Finally, we show that this junction can be tuned so as to provide for complete rectification of the time-averaged Josephson current-phase relation.