Predicted Very Large Thermoelectric Effect in Ferromagnet-Superconductor Junctions in the Presence of a Spin-Splitting Magnetic Field

Abstract

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.

Thermal conductance by Dirac fermions in a normal-insulator-superconductor junction of silicene

“…Up to now, no experiment has been carried out in the context of proximity effect in silicene. On the other hand, heat transport in Dirac systems 33,34 and superconducting hybrid structures also has become an active field of research over the past decade [35][36][37] . Thermal conductance (TC) has been investigated in graphene based hybrid junctions in Ref.…”

Nonlinear electric and thermoelectric Andreev transport through a hybrid quantum dot coupled to ferromagnetic and superconducting leads

“…Firstly, we discuss the spin-dependent CPs with a nonzero polarization p. Figure 2 displays the solutions of equations (19), (20), (21) and (22) as a function of ε d with p = 0 and p = 0.9, for S-dominant [(a),(b)] and F-dominant [(c),(d)] cases. Nonzero polarization generally separates CPs, i.e., u L↑ = u L↓ and z L↑ = z L↓ .…”

Proposal for a phase-coherent thermoelectric transistor

“…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][4][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.…”

“…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 Fig. 1(a).…”

“…In such a case one avoids the mismatch of the Fermi velocities at the interfaces, meaning the proximity effect between the bulky part of the loop and the constriction is increased. 4 . Our device, however, allows to approach this maximum value at finite T by tuning the magnetic flux.…”