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Journal of Applied Physics

Out-of-phase Andreev transports in a double-quantum-dot Cooper-pair splitter

Wei‐Jiang Gong, Xiaoqi Wang, Yu-Lian Zhu, Zhen Gao, Haina Wu

Published Jun 3, 2016• 8 citations
Publisher

Abstract

We investigate the Andreev transports through a double-quantum-dot Cooper-pair splitter with an additional direct coupling between the dots. It is found that when finite magnetic flux is applied through this structure, its induced phase adjusts the local and crossed Andreev reflections in different manners. Moreover, in the presence of appropriate magnetic flux, the crossed Andreev reflection can be efficiently enhanced, accompanied by the suppression of the local Andreev reflection. Such a result exists in both the linear and nonlinear transport regions, even in the case of strong intradot Coulomb interaction. Therefore, such a work provides a promising scheme to enhance the splitting of the Cooper pair.

DOI
10.1063/1.4953214

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cond-mat.mes-hallCross-listedarXiv:2608.26702•Aug 28, 2026
We investigate the Andreev transports through a double-quantum-dot Cooper-pair splitter with an additional direct coupling between the dots. It is found that when finite magnetic flux is applied through this structure, its induced phase adjusts the local and crossed Andreev reflections in different manners. Moreover, in the presence of appropriate magnetic flux, the crossed Andreev reflection can be efficiently enhanced, accompanied by the suppression of the local Andreev reflection. Such a result exists in both the linear and nonlinear transport regions, even in the case of strong intradot Coulomb interaction. Therefore, such a work provides a promising scheme to enhance the splitting of the Cooper pair.
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.
Abstract Entanglement of electrons is studied by means of current–current correlations in two Cooper pair splitter devices: with one and two proximized quantum dots (1QD and 2QD), in presence of intra- and inter-dot Coulomb interactions, and weakly coupled with metallic electrodes. The 1QD system, where Cooper pairs can be transmitted to the same or split to different normal electrodes, is contrasted with the 2QD device, where double occupancy of a single quantum dot is forbidden and transport is only through an inter-dot singlet due to non-local crossed Andreev reflection processes deep in the superconducting energy gap. Separating the current correlation function into components for partial currents of electrons and holes through various Andreev bound states, one can see bunching and antibunching of split particles: inter-level components between electron and hole currents flowing to different electrodes are positive, while intra-level electron–electron or hole–hole components are negative, respectively. Spectral decomposition of the frequency-dependent current cross-correlation is performed to get better insight into mechanisms of entanglement and dynamics of split Cooper pairs, and to extract various charge fluctuation processes with different relaxation times, related to electron and hole currents flowing through the Andreev bound states. Only low frequency polarization fluctuations are seen in the current cross-correlations, while various negative and positive high frequency (charge fluctuations) components compensate each other in the symmetric system.
Cooper pairs in the superconductor are a natural source of spin entanglement. The existing proposals of the Cooper pair splitter can only realize a low efficiency of entanglement production, and its size is constrained by the superconducting coherence length. Here we show that a long-range Cooper pair splitter can be implemented in a normal metal-superconductor-normal metal (NSN) junction by driving a supercurrent in the S. The supercurrent results in a band gap modification of the S, which significantly enhances the crossed Andreev reflection (CAR) of the NSN junction and simultaneously quenches its elastic cotunneling. Therefore, a high entanglement production rate close to its saturation value can be achieved by the inverse CAR. Interestingly, in addition to the conventional entangled electron states between opposite energy levels, novel entangled states with equal energy can also be induced in our proposal.
In this Letter, we manipulate the phase shift of a Josephson junction using a parallel double quantum dot (QD). By employing a superconducting quantum interference device, we determine how orbital hybridization and detuning affect the current-phase relation in the Coulomb blockade regime. For weak hybridization between the QDs, we find π junction characteristics if at least one QD has an unpaired electron. Notably the critical current is higher when both QDs have an odd electron occupation. By increasing the inter-QD hybridization the critical current is reduced, until eventually a π-0 transition occurs. A similar transition appears when detuning the QD levels at finite hybridization. Based on a zero-bandwidth model, we argue that both cases of phase-shift transitions can be understood considering an increased weight of states with a double occupancy in the ground state and with the Cooper pair transport dominated by local Andreev reflection.
We show how superconductors can be used to couple, initialize, and read out spatially separated spin qubits. When two single-electron quantum dots are tunnel coupled to the same superconductor, the singlet component of the two-electron state partially leaks into the superconductor via crossed Andreev reflection. This induces a gate-controlled singlet-triplet splitting which, with an appropriate superconductor geometry, remains large for dot separations within the superconducting coherence length. Furthermore, we show that when two double-dot singlet-triplet qubits are tunnel coupled to a superconductor with finite charging energy, crossed Andreev reflection enables a strong two-qubit coupling over distances much larger than the coherence length.
Generating non-locally entangled electron pairs via Cooper-pair splitting is vital for solid-state quantum information processing. However, isolating the underlying crossed Andreev reflection (CAR) is challenging due to competing transport processes like electron tunneling (ET) and local Andreev reflection (AR). Here, we propose a flux-tunable four-terminal normal metal-superconductor junction that achieves deterministic, 100\% efficient CAR. We demonstrate that at exactly half a magnetic flux quantum (φ=πφ=πφ=π), exact destructive Aharonov-Bohm and Peierls interferences structurally forbid ET and AR respectively. By tuning the central junction hopping, electron reflection is also suppressed to zero. Using the Cauchy argument principle, we prove that this suppression manifests as a quantized topological winding number, guaranteeing a topologically protected unit CAR probability. We establish that this regime is characterized by a strictly positive cross-correlation shot noise, providing an unambiguous experimental signature of Cooper-pair splitting. Furthermore, this perfect CAR is nearly broadband within the superconducting gap and remarkably robust against structural disorder, offering a highly resilient architecture for deterministic nonlocal entanglement generation.