  It has recently been proposed and experimentally demonstrated that it is
possible to generate large thermoelectric effects in ferromagnet/superconductor
structures due to a spin-dependent particle-hole asymmetry. Here, we
theoretically show that quasiparticle tunneling between two spin-split
superconductors enhances the thermoelectric response manyfold compared to when
only one such superconductor is used, generating Seebeck coefficients
($\mathcal{S} > 1$ mV/K) and figures of merit ($ZT \simeq 40$) far exceeding
the best bulk thermoelectric materials, and also becomes more resilient toward
inelastic scattering processes. We present a generalized Onsager
response-matrix which takes into account spin-dependent voltage and temperature
gradients. Moreover, we show that thermally induced spin currents created in
such junctions, even in the absence of a polarized tunneling barrier, also
become largest in the case where a spin-dependent particle-hole asymmetry
exists on both sides of the barrier. We determine how these thermal spin
currents can be tuned both in magnitude and sign by several parameters,
including the external field, temperature, and the superconducting
phase-difference.
