Multi-terminal superconducting Josephson junctions based on the proximity effect offer the bright opportunity to tailor non trivial quantum states in nanoscale weaklinks. These structures can realize exotic topologies in multidimensions [1] as, for example, artificial topological superconductors able to support Majorana bound states [2,3], and pave the way to emerging quantum technologies [4][5][6][7] and future quantum information schemes [8]. Here, we report the first realization of a three-terminal Josephson interferometer based on a proximized nanosized weak-link. Our tunneling spectroscopy measurements reveal transitions between gapped (i.e., insulating) and gapless (i.e., conducting) states, those being controlled by the phase configuration of the three superconducting leads connected to the junction. We demonstrate the topological nature of these transitions: a gapless state necessarily occurs between two gapped states of different topological index, very much like the interface between two insulators of different topology is necessarily conducting [9]. The topological numbers characterizing such gapped states are given by superconducting phase windings over the two loops forming the Josephson interferometer. Since these gapped states cannot be transformed to one another continuously withouth passing through a gapless condition, these are topologically protected. Our observation of the gapless state is pivotal for enabling phase engineering of more sophisticated artificial topological materials realizing Weyl points or the anomalous Josephson effect [1,[4][5][6][7]10].When two superconductors (S) are coupled through a normal metal (N), they realize a Josephson junction (JJ) and superconducting correlations are induced in the N region due to proximity effect [11][12][13][14][15][16]. As a consequence, the N metal acquires genuine superconducting-like properties such as the ability to sustain a supercurrent, and a gap in the density of states (DoS) whose amplitude can be controlled by the macroscopic phase difference between the S leads [12,[17][18][19]. This process therefore enables the N region to possess a character ranging from insulating-like (gapped state) to conductinglike (gapless state) [14,17].Although two-terminal JJs based on proximity effect have been at the focus of an intense research for several years [11][12][13][14][15][16][17][18][19][20][21] weak-links [10]. Yet, the impact and control over three superconducting phases acting on a nanosized N region have never been explored so far despite recent predictions of using multi-terminal JJs for tailoring and controlling exotic quantum states. [1,4,6,10]. Indeed, multi-terminal (>2) JJs allow the spin-orbit interaction to affect substantially the Andreev bound levels enabling the manipulation of electrons in sinarXiv:1603.00338v1 [cond-mat.mes-hall]

Gate-tunable Josephson junctions (JJs) are the backbone of superconducting classical and quantum computation. Typically, these systems exploit low charge concentration materials, and present technological difficulties limiting their scalability. Surprisingly, electric field modulation of supercurrent in metallic wires and JJs has been recently demonstrated. Here, we report the realization of titanium-based monolithic interferometers which allow tuning both JJs independently via voltage bias applied to capacitively-coupled electrodes. Our experiments demonstrate full control of the amplitude of the switching current (IS) and of the superconducting phase across the single JJ in a wide range of temperatures. Astoundingly, by gate-biasing a single junction the maximum achievable total IS suppresses down to values much lower than the critical current of a single JJ. A theoretical model including gate-induced phase fluctuations on a single junction accounts for our experimental findings. This class of quantum interferometers could represent a breakthrough for several applications such as digital electronics, quantum computing, sensitive magnetometry and single-photon detection.The possibility of tuning the properties of Bardeen-Cooper-Schrieffer (BCS) metallic superconductors via conventional gating has been excluded for almost a century. Surprisingly, strong static electric fields have been recently shown to modulate the supercurrent down to full suppression and even to induce a superconductorto-normal phase transition in metallic wires [1,2] and Josephson junctions (JJs) [3-5] without affecting their normal-state behavior. Yet, these results did not find a microscopic theoretical explanation so far [6]. In this Article, we lay down a fundamental brick for both the insight and the technological application of this unorthodox field-effect by realizing a titanium-based monolithic superconducting quantum interference device (SQUID) which can be tuned by applying a gate bias to both JJs independently. We first show modulation of the amplitude and the position of the interference pattern of the switching current (I S ) by acting with an external electric field on a single junction of the interferometer. Notably, this phenomenology differs from that of conventional gatetunable SQUIDs [7-10] and cannot be explained by a simple squeezing of the critical current of the junction induced by the electric field [11]. Consequently, a local electric field acts on a global scale influencing the properties of both JJs. Since the superconducting phases of the two JJs are non-locally connected by fluxoid quantization, we deduce that the electric field must act both on the critical current amplitude and couple to the superconducting phase across the single junction. The overall interferometer phase can shift from −0.4π to 0.2π depending on the used gate electrode and on the strength of the gate bias. Furthermore, the effect persists up to ∼ 80% of the superconducting critical temperature.Fully-metallic field-effect controllable Josephson...

Coherent transport properties of a three-terminal hybrid superconducting interferometerVischi, F.; Carrega, M.; Strambini, E.; D'Ambrosio, S.; Bergeret, F. S.; Nazarov, Yuli; Giazotto, F. Important noteTo cite this publication, please use the final published version (if applicable). Please check the document version above. CopyrightOther than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policyPlease contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. We present an exhaustive theoretical analysis of a double-loop Josephson proximity interferometer, such as the one recently realized by Strambini et al. for control of the Andreev spectrum via an external magnetic field. This system, called ω-SQUIPT, consists of a T-shaped diffusive normal metal (N ) attached to three superconductors (S) forming a double-loop configuration. By using the quasiclassical Green-function formalism, we calculate the local normalized density of states, the Josephson currents through the device, and the dependence of the former on the length of the junction arms, the applied magnetic field, and the S/N interface transparencies. We show that by tuning the fluxes through the double loop, the system undergoes transitions from a gapped to a gapless state. We also evaluate the Josephson currents flowing in the different arms as a function of magnetic fluxes, and we explore the quasiparticle transport by considering a metallic probe tunnel-coupled to the Josephson junction and calculating its I -V characteristics. Finally, we study the performances of the ω-SQUIPT and its potential applications by investigating its electrical and magnetometric properties.

We discuss the quasiparticle entropy and heat capacity of a dirty superconductor-normal metalsuperconductor junction. In the case of short junctions, the inverse proximity effect extending in the superconducting banks plays a crucial role in determining the thermodynamic quantities. In this case, commonly used approximations can violate thermodynamic relations between supercurrent and quasiparticle entropy. We provide analytical and numerical results as a function of different geometrical parameters. Quantitative estimates for the heat capacity can be relevant for the design of caloritronic devices or radiation sensor applications.

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A superconductor/normal metal/superconductor Josephson junction is a coherent electron system where the thermodynamic entropy depends on temperature and difference of phase across the weak-link. Here, exploiting the phase-temperature thermodynamic diagram of a thermally isolated system, we argue that a cooling effect can be achieved when the phase drop across the junction is brought from 0 to π in a iso - entropic process. We show that iso - entropic cooling can be enhanced with proper choice of geometrical and electrical parameters of the junction, i.e. by increasing the ratio between supercurrent and total junction volume. We present extensive numerical calculations using quasi-classical Green function methods for a short junction and we compare them with analytical results. Interestingly, we demonstrate that phase-coherent thermodynamic cycles can be implemented by combining iso - entropic and iso - phasic processes acting on the weak-link, thereby engineering the coherent version of thermal machines such as engines and cooling systems. We therefore evaluate their performances and the minimum temperature achievable in a cooling cycle.

We study the thermodynamic properties of a superconductor/normal metal/superconductor Josephson junction in the short limit. Owing to the proximity effect, such a junction constitutes a thermodynamic system where phase difference, supercurrent, temperature and entropy are thermodynamical variables connected by equations of state. These allow conceiving quasi-static processes that we characterize in terms of heat and work exchanged. Finally, we combine such processes to construct a Josephson-based Otto and Stirling cycles. We study the related performance in both engine and refrigerator operating mode.