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arXiv:2306.05758 · Physical Review Letters

Interplay of Andreev Reflection and Coulomb Blockade in Hybrid Superconducting Single-Electron Transistors

Laura Sobral Rey, David Christian Ohnmacht, Clemens B. Winkelmann, Jens Siewert, Wolfgang Belzig, Elke Scheer

Published Feb 2, 2024• 5 citations
arXivHTMLPDF

Abstract

We study the interplay between Coulomb blockade and superconductivity in a tunable superconductor-superconductor-normal-metal single-electron transistor. The device is realized by connecting the superconducting island via an oxide barrier to the normal-metal lead and with a break junction to the superconducting lead. The latter enables Cooper pair transport and (multiple) Andreev reflection. We show that these processes are relevant also far above the superconducting gap and that signatures of Coulomb blockade may reoccur at high bias while they are absent for small bias in the strong-coupling regime. Our experimental findings agree with simulations using a rate equation approach in combination with the full counting statistics of multiple Andreev reflection.

DOI
10.1103/physrevlett.132.057001

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We study the interplay between Coulomb blockade and superconductivity in a tunable superconductor-superconductor-normal-metal single-electron transistor. The device is realized by connecting the superconducting island via an oxide barrier to the normal-metal lead and with a break junction to the superconducting lead. The latter enables Cooper pair transport and (multiple) Andreev reflection. We show that these processes are relevant also far above the superconducting gap and that signatures of Coulomb blockade may reoccur at high bias while they are absent for small bias in the strong-coupling regime. Our experimental findings agree with simulations using a rate equation approach in combination with the full counting statistics of multiple Andreev reflection.
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We propose and analyze a spin-entangler for electrons based on an s-wave superconductor coupled to two quantum dots, each of which is coupled to normal Fermi leads. We show that in the presence of a voltage bias and in the Coulomb blockade regime two correlated electrons provided by the Andreev process can coherently tunnel from the superconductor via different dots into different leads. The spin singlet coming from the Cooper pair remains preserved in this process, and the setup provides a source of mobile and nonlocal spin-entangled electrons. The transport current is calculated and shown to be dominated by a two-particle Breit-Wigner resonance that allows the injection of two spin-entangled electrons into different leads at exactly the same orbital energy, which is a crucial requirement for the detection of spin entanglement via noise measurements. The coherent tunneling of both electrons into the same lead is suppressed by the on-site Coulomb repulsion and/or the superconducting gap, while the tunneling into different leads is suppressed through the initial separation of the tunneling electrons. In the regime of interest the particle-hole excitations of the leads are shown to be negligible. The Aharonov-Bohm oscillations in the current are shown to contain single- and two-electron periods with amplitudes that both vanish with increasing Coulomb repulsion albeit differently fast.
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The manipulation of single charge quanta in solid state systems has been a field of active interest for several decades. At the basis of such structures lays the Coulombic repulsion between electrons in a small metallic island yielding the so-called Coulomb-blockade regime. Many quantum phenomena, such as the tunnelling effect or the Josephson coupling in superconducting junctions, have been exploited so far to control the charging state of a conducting island, and enable a number of applications ranging from on-chip cooling and current generation to single-photon detection. Yet, in all Coulombic systems the external control parameters play a crucial role, reaching sometimes a rather complex experimental configuration. Here we show that quantum interference established in a superconducting nanowire can provide a phase-tunable energy barrier which allows charge manipulation with enhanced functionalities. This additional degree of freedom for single electronics stems from the coupling between magnetic flux-dependent proximity effect and charging levels discretization present in a Coulomb-blockaded island. Our quantum interference nanostructure represents the first realization of a superconducting hybrid single-electron transistor called SQUISET in which the charging landscape is phase-coherently manipulated by an external magnetic flux. The interferometric nature of the transistor adds new perspectives to single electronics making it a promising alternative building block in quantum metrology, coherent caloritronics, and quantum information technology.
We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even-odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasiparticle tunneling rates are comparable to the coherent Cooper pair oscillation frequency. Furthermore, the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.