Giant thermoelectric effects in a proximity-coupled superconductor–ferromagnet device

Abstract

The usually negligibly small thermoelectric effects in superconducting heterostructures can be boosted dramatically due to the simultaneous effect of spin splitting and spin filtering. Building on an idea of our earlier work (Machon et al 2013 Phys. Rev. Lett. 110 047002), we propose realistic mesoscopic setups to observe thermoelectric effects in superconductor heterostructures with ferromagnetic interfaces or terminals. We focus on the Seebeck effect being a direct measure of the local thermoelectric response and find that a thermopower of the order of ∼250 μ − V K 1 can be achieved in a transistor-like structure. A measurement of the thermopower can furthermore be used to determine quantitatively the spin-dependent interface parameters that induce the spin splitting. For applications in nanoscale cooling we discuss the figure of merit for which we find values exceeding 1.5 for temperatures ≲1 K.Keywords: thermopower, figure of merit, proximity effect, quasiclassical theory, spin-dependent boundary conditionsSince their discovery at the beginning of the 19th century [1-4], thermoelectric effects have attracted continued attention in physics, as they provide the basis for a large variety of devices used in a multitude of fields in physics and engineering connected with energy management and harvesting. The coupling of thermal and electric transport equations is also a basic concept in (k B is the Boltzmann constant and T the temperature) around the chemical potential. As consequence, in standard metals, described by Fermi-liquid theory, thermoelectric effects are strongly suppressed at temperatures well below the Fermi temperature, since the single-particle DOS and the scattering rates vary on a much larger energy scale than k T B . We note that, in contrast, in nanoscale conductors even in the simple Landauer picture of free electrons the transmission function may depend considerably on energy, e.g. in quantum dots or due to interaction effects, and can lead to a sizable thermoelectric effect [14][15][16]. The same holds for strongly correlated metals with a strong variation of the DOS at the Fermi level and for semiconductors with a Fermi level near the bottom or top of an energy band.However, with regard to thermoelectric effects in superconductors the situation is less favorable. The most widely used Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity [17] is essentially build on top of a deeply degenerate Fermi gas. This is reflected in the almost perfect electron-hole symmetry in the standard version of the theory, appropriate for conventional low-temperature superconductors, suppressing thermoelectric effects [18,19]. On the other hand, supercurrents can interfere with thermal currents and generate a thermoelectric voltage in interferometer geometries [18]. Here the effect is essentially related to the temperature dependence of the supercurrent. Later this effect was considered further in mesoscopic Andreev interferometers [20][21][22][23][24] and used to explain partially the experimental finding...

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