We show that a huge thermoelectric effect can be observed by contacting a superconductor whose density of states is spin-split by a Zeeman field with a ferromagnet with a non-zero polarization. The resulting thermopower exceeds kB/e by a large factor, and the thermoelectric figure of merit ZT can far exceed unity, leading to heat engine efficiencies close to the Carnot limit. We also show that spin-polarized currents can be generated in the superconductor by applying a temperature bias.PACS numbers: 74.25.fg, 74.25.F-, 72.25.-b Thermoelectric effects, electric potentials generated by temperature gradients and vice versa, are intensely studied because of their possible use in converting the waste heat from various processes to useful energy. The conversion efficiency η =Ẇ /Q, the ratio of output powerẆ to the rate of thermal energy consumedQ, in thermoelectric devices however typically falls short of the theoretical Carnot limit and is low compared to other heat engines, which has motivated an extensive search for better materials. [1] In electronic conductors a major contributor to thermoelectricity is breaking of the symmetry between positive and negative-energy charge carriers (electrons and holes, respectively) [2]. Within Sommerfeld expansion, this is described by the Mott relation [3], which predicts thermoelectric effects of the order ∼ k B T /E 0 , where T is the temperature and E 0 a microscopic energy scale describing the energy dependence in the transport. This is usually a large atomic energy scale (in metals, the Fermi energy), so that E 0 k B T even at room temperature and these effects are often weak. Larger electron-hole asymmetries are however attainable in semiconductors, as the chemical potential can be tuned close to the band edges, where the density of states varies rapidly. [1,4] The situation in superconductors is superficially similar to semiconductors. The quasiparticle transport is naturally strongly energy dependent due to the presence of the energy gap ∆, which can be significantly smaller than atomic energy scales. However, the chemical potential is not tunable in the same sense as in semiconductors, as charge neutrality dictates that electron-hole symmetry around the chemical potential is preserved. This implies that the thermoelectric effects in superconductors are often even weaker than in the corresponding normal state, in addition to being masked by supercurrents [5,6].We show in this Letter that this problem can be overcome in a conventional superconductor by applying a spin-splitting field h. It shifts the energies of electrons with parallel and antiparallel spin orientations to opposite directions. [7] This breaks the electron-hole symmetry for each spin separately, but conserves charge neutrality, as the total density of states remains electron-hole symmetric. In this situation, thermoelectric effects can be obtained by coupling the superconductor to a spinpolarized system.

There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number of problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for testing near-term quantum annealers and other quantum algorithmic strategies for optimization problems.

Spin selectivity in a ferromagnet results from a difference in the density of up-and down-spin electrons at the Fermi energy as a consequence of which the scattering rates depend on the spin orientation of the electrons. This property is utilized in spintronics to control the flow of electrons by ferromagnets in a ferromagnet (F1)/normal metal (N)/ferromagnet (F2) spin valve, where F1 acts as the polarizer and F2 the analyser. The feasibility of superconducting spintronics depends on the spin sensitivity of ferromagnets to the spin of the equal spintriplet Cooper pairs, which arise in superconductor (S)-ferromagnet (F) heterostructures with magnetic inhomogeneity at the S-F interface. Here we report a critical temperature dependence on magnetic configuration in current-in-plane F-S-F spin valves with a holmium spin mixer at the S-F interface providing evidence of a spin selectivity of the ferromagnets to the spin of the triplet Cooper pairs.

Efficient electron-refrigeration based on a normal-metal/spin-filter/superconductor junction is proposed and demonstrated theoretically. The spin-filtering effect leads to values of the cooling power much higher than in conventional normal-metal/nonmagnetic-insulator/superconductor coolers and allows for an efficient extraction of heat from the normal metal. We demonstrate that highly efficient cooling can be realized in both ballistic and diffusive multi-channel junctions in which the reduction of the electron temperature from 300 mK to around 50 mK can be achieved. Our results indicate the practical usefulness of spin-filters for efficiently cooling detectors, sensors, and quantum devices. PACS numbers:The flow of charge current in N/I/S (normal metal/insulator/ superconductor) tunnel junctions at a bias voltage V is accompanied by a heat transfer from N into S. This phenomenon arises due to presence of the superconducting energy-gap ∆ which allows for a selective tunneling of high-energy "hot" quasiparticles out of N. Such a heat transfer through N/I/S junctions can be used for the realization of microcoolers. [1][2][3][4] Present state-of-the-art experiments allow the reduction of the electron temperature in a normal metal lead from 300 to about 100 mK, offering perspectives for on-chip cooling of nano or micro systems, such as high-sensitive sensors, detectors and quantum devices. [5][6][7] However, a serious limitation of the performance of N/I/S microcoolers arises from the intrinsic multi-particle nature of charge transport in N/I/S junctions which is governed not only by single-particle tunneling but also by two-particle processes due to the Andreev reflection.3 While the single-particle current and the associated heat current are due to quasiparticles with energies E > ∆, at low temperatures or high junction transparencies the charge transport in N/I/S junctions is dominated by a subgap process: the Andreev reflection. In such a process, electrons with energies smaller than ∆ are reflected as holes at the N/I/S interface, leading to the transfer of a Cooper pair into the superconductor. Since the energy of the electrons and holes involved in the process are symmetric with respect to the Fermi energy, there is no heat current through the interface. However, by applying a subgap bias across the junctions the Andreev reflection results in a finite charge current I A flowing through the N/I/S system. Due to finite resistance of the normal metal, this current generates Joule heating I A V , which is entirely deposited in the normal metal. [8][9][10] This heating exceeds the single-particle cooling at temperatures low enough, and therefore the suppression of Andreev processes is desirable for an efficient cooling.One way to decrease the Andreev current is by decreasing the N/I/S junction transparency. However, large contact resistance hinders "hot" carrier transfer and leads to a severe limitation in the achievable cooling powers. In order to increase the junction transparency and at the same time to reduce ...