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arXiv:cond-mat/0111209 · Physical review. B, Condensed matter

Probing spin states of coupled quantum dots by a dc Josephson current

Yu Zhu, Qing‐Feng Sun, Tsung-han Lin

Published Aug 9, 2002• 21 citations
arXivHTMLPDF

Abstract

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 $N=1,3$ (odd), the supercurrent will reverse its sign if the CQD becomes a magnetic molecule; for a CQD with $N=2$ (even), the supercurrent will decrease sharply around the transition between the spin singlet and triplet ground states of the CQD.

DOI
10.1103/physrevb.66.085306

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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.
We study a double quantum dot, each dot of which is tunnel coupled to superconducting leads. In the Coulomb blockade regime, a spin-dependent Josephson coupling between two superconductors is induced, as well as an antiferromagnetic Heisenberg exchange coupling between the spins on the double dot that can be tuned by the superconducting phase difference. We show that the correlated spin states---singlet or triplets---on the double dot can be probed via the Josephson current in a dc-superconducting quantum interference device setup.
We study the spin-spin coupling between two single-electron quantum dots due to the Coulomb and spin-orbit interactions, in the absence of tunneling between the dots. We find an anisotropic XYXYXY spin-spin interaction that is proportional to the Zeeman splitting produced by the external magnetic field. This interaction is studied both in the limit of weak and strong Coulomb repulsion with respect to the level spacing of the dot. The interaction is found to be a nonmonotonic function of interdot distance a0{a}_{0}a0​ and external magnetic field and, moreover, vanishes for some special values of a0{a}_{0}a0​ and/or magnetic field orientation. This mechanism thus provides a new way to generate and tune spin interaction between quantum dots. We propose a scheme to measure this spin-spin interaction based on the spin-relaxation-measurement technique.
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.
We analyze coherent spin rotations in a dc biased double quantum dot driven by crossed dc and ac magnetic fields. In this configuration, spatial delocalization due to interdot tunneling competes with intradot spin rotations induced by the time dependent magnetic field, giving rise to a complicated time dependent behavior of the tunneling current. When the Zeeman splitting has the same value in both dots and spin flip is negligible, the electrons remain in the triplet subspace performing coherent spin rotations and current does not flow. This electronic trapping is removed either by finite spin relaxation or when the Zeeman splitting is different in each quantum dot. In the last case, we will show that by applying a resonant bichromatic magnetic field, the electrons become trapped in a coherent superposition of states and electronic transport is blocked. Then, manipulating ac magnetic fields allows one to drive electrons to perform coherent spin rotations which can be unambiguously detected by direct measurement of the tunneling current.
We determine the spin-exchange coupling J between two electrons located in two vertically tunnel-coupled quantum dots, and its variation when magnetic (B) and electric (E) fields (both in-plane and perpendicular) are applied. We predict a strong decrease of J as the in-plane B field is increased, mainly due to orbital compression. Combined with the Zeeman splitting, this leads to a singlet-triplet crossing, which can be observed as a pronounced jump in the magnetization at in-plane fields of a few T, and perpendicular fields of the order of 10 T for typical self-assembled dots. We use harmonic potentials to model the confining of electrons, and calculate the exchange J using the Heitler-London and Hund-Mulliken techniques, including the long-range Coulomb interaction. With our results we provide experimental criteria for the distinction of singlet and triplet states, and therefore for microscopic spin measurements. In the case where dots of different sizes are coupled, we present a simple method to switch the spin coupling on and off with exponential sensitivity using an in-plane electric field. Switching the spin coupling is essential for quantum computation using electronic spins as qubits.