Identifying materials and devices which offer efficient thermoelectric effects at low temperature is a major obstacle for the development of thermal management strategies for low-temperature electronic systems. Superconductors cannot offer a solution since their near perfect electron-hole symmetry leads to a negligible thermoelectric response; however, here we demonstrate theoretically a superconducting thermoelectric transistor which offers unparalleled figures of merit of up to ∼ 45 and Seebeck coefficients as large as a few mV/K at sub-Kelvin temperatures. The device is also phasetunable meaning its thermoelectric response for power generation can be precisely controlled with a small magnetic field. Our concept is based on a superconductor-normal metal-superconductor interferometer in which the normal metal weak-link is tunnel coupled to a ferromagnetic insulator and a Zeeman split superconductor . Upon application of an external magnetic flux, the interferometer enables phase-coherent manipulation of thermoelectric properties whilst offering efficiencies which approach the Carnot limit.It is known that electron-hole symmetry breaking is essential for a material to posses a finite thermoelectric figure of merit 1,2 . In principle, conventional superconductors have a near perfect symmetric spectrum and therefore are not suitable for thermoelectric devices. However, if the density of states is spin-split by a Zeeman field a superconductor-ferromagnet hybrid device can provide a thermoelectric effect 3-5 with a figure of merit close to 1. Here we propose a multifunctional phase-coherent superconducting transistor in which the thermoelectric efficiency is tunable through an externally applied magnetic flux. A giant Seebeck coefficient of several mV/K and a figure of merit close to ∼ 45 is predicted for realistic materials parameters and materials combinations.The phase-coherent thermoelectric transistor is based on two building blocks. The first one is sketched in Fig. 1(a) and consists of a superconducting film (S R ) tunnel-coupled to a normal metal (N) by a ferromagnetic insulator (FI). The latter induces an exchange field (h) in S R which leads to a Zeeman spin-split superconducting DoS. The spectrum for spin-up (↑) and spin-down (↓) electrons is given bywhere| is the conventional Bardeen-Cooper-Schrieffer DoS in a superconductor, E is the energy, ∆ R is the order parameter, and Γ accounts for broadening. Due to the presence of the spin-splitting field, ∆ R depends on temperature (T ) and h. While the total DoS of S R , ν S R (E) = ν S R↑ (E) + ν S R↓ (E), is electron-hole symmetric [ Fig. 1(b)], the spin-dependent a) Electronic mail: giazotto@sns.it b) Electronic mail: jjr33@cam.ac.uk c) Electronic mail: sebastian bergeret@ehu.es ν S R↑(↓) (E) components are no longer even functions of the energy. This means that electron-hole imbalance can, in principle, be achieved using a spin-filter contact with a normal metal. This would yield a finite thermoelectric effect 3,4 in the N/FI/S R heterostructure shown in F...

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A hybrid superconductor--two-dimensional electron gas microdevice is presented. Its working principle is based on the suppression of Andreev reflection at the superconductor-semiconductor interface caused by a magnetic barrier generated by a ferromagnetic strip placed on top of the structure. Device switching is predicted with fields up to some mT and working frequencies of several GHz, making it promising for applications ranging from microswitches and storage cells to magnetic field discriminators.Comment: 4 pages, 3 figures, minor changes to tex

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