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Physical Review B

Control of the supercurrent through a parallel-coupled double quantum dot system

Hui Pan, Tsung-han Lin

Published Dec 12, 2006• 35 citations
Publisher

Abstract

The supercurrent through parallel-coupled double quantum dots connected to two superconductor leads is investigated theoretically. The possibility of controlling the supercurrent of the system is explored by tuning the interdot coupling, dot energy levels, total magnetic flux treading the ring connecting dots and leads, and flux difference between two subrings. Owing to the interdot coupling, one strongly and one weakly coupled states of the system can be formed. The magnetic flux can exchange the function of the two states, which leads to a swap effect. It is found that the oscillation period of the supercurrent with respect to the magnetic flux depends not only on the flux difference but also on the ratio of the two parts fluxes.

DOI
10.1103/physrevb.74.235312

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The supercurrent through parallel-coupled double quantum dots connected to two superconductor leads is investigated theoretically. The possibility of controlling the supercurrent of the system is explored by tuning the interdot coupling, dot energy levels, total magnetic flux treading the ring connecting dots and leads, and flux difference between two subrings. Owing to the interdot coupling, one strongly and one weakly coupled states of the system can be formed. The magnetic flux can exchange the function of the two states, which leads to a swap effect. It is found that the oscillation period of the supercurrent with respect to the magnetic flux depends not only on the flux difference but also on the ratio of the two parts fluxes.
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.
Serial double quantum dots created in semiconductor nanostructures provide a versatile platform for investigating two-electron spin quantum states, which can be tuned by electrostatic gating and an external magnetic field. In this Rapid Communication, we directly measure the supercurrent reversal between adjacent charge states of an InAs nanowire double quantum dot with superconducting leads, in good agreement with theoretical models. In the even charge parity sector, we observe a supercurrent blockade with increasing magnetic field, corresponding to the spin singlet to triplet transition. Our results demonstrate a direct spin to supercurrent conversion, the superconducting equivalent of the Pauli spin blockade. This effect can be exploited in hybrid quantum architectures coupling the quantum states of spin systems and superconducting circuits.
Exact eigenstates of the parallel coupled double quantum dots attached to the non-interacting leads taken in zero-bandwidth limit are analytically obtained in each particle and spin sector. The ground state of the half-filled system is identified from a four dimensional subspace of the twenty dimensional Hilbert space for different values of tunable parameters of the system viz. the energy levels of the quantum dots, the interdot tunneling matrix-element, the ondot and interdot Coulomb interactions and quantities like spin-spin correlation between the dots, occupancies of the dots are calculated. In the parameter space of the interdot tunneling matrix-element and ondot Coulomb interaction, the dots exhibit both ferromagnetic and antiferromagnetic correlation. There is a critical dependency of the interdot tunneling matrix-element on the ondot Coulomb interaction which leads to transition from the ferromagnetic correlation to the antiferromagnetic correlation as the interdot tunneling matrix-element is increased. The ferromagnetic and antiferromagnetic correlations also exist in the absence of interdot tunneling matrix-element through indirect exchange via the leads. The interdot Coulomb interaction is found to affect this dependency considerably.
We investigate the idea for probing spin states of two coupled quantum dots (CQDs) by the dc Josephson current flowing through them. This theory requires weak coupling between CQDs and electrodes, but allows arbitrary interdot tunnel coupling, intradot and interdot Coulomb interactions. We find that the Coulomb blockade peaks exhibit a nonmonotonous dependence on the Zeeman splitting of CQDs, which can be understood in terms of Andreev bound states. More importantly, the supercurrent in the Coulomb blockade valleys may provide information on the spin states of CQDs: for CQDs with total electron number N=1,3N=1,3N=1,3 (odd), the supercurrent will reverse its sign if the CQD becomes a magnetic molecule; for a CQD with N=2N=2N=2 (even), the supercurrent will decrease sharply around the transition between the spin singlet and triplet ground states of the CQD.
Strong electron and spin correlations in a double quantum dot (DQD) can give rise to different quantum states. We observe a continuous transition from a Kondo state exhibiting a single-peak Kondo resonance to another exhibiting a double peak by increasing the interdot coupling (t) in a parallel-coupled DQD. The transition into the double-peak state provides evidence for spin entanglement between the excess electrons on each dot. Toward the transition, the peak splitting merges and becomes substantially smaller than t because of strong Coulomb effects. Our device tunability bodes well for future quantum computation applications.
We consider the subgap physics of a hybrid double-quantum dot Cooper-pair splitter with large single-level spacings, in the presence of tunneling between the dots and finite Coulomb intra- and interdot Coulomb repulsion. In the limit of a large superconducting gap, we treat the coupling of the dots to the superconductor exactly. We employ a generalized master-equation method, which easily yields currents, noise, and cross-correlators. In particular, for finite inter- and intradot Coulomb interaction, we investigate how the transport properties are determined by the interplay between local and nonlocal tunneling processes between the superconductor and the dots. We examine the effect of interdot tunneling on the particle-hole symmetry of the currents with and without spin-orbit interaction. We show that spin-orbit interaction in combination with finite Coulomb energy opens the possibility to control the nonlocal entanglement and its symmetry (singlet/triplet). We demonstrate that the generation of nonlocal entanglement can be achieved even without any direct nonlocal coupling to the superconducting lead.