Thermoelectricity carried by proximity-induced odd-frequency pairing in ferromagnet/superconductor junctions

We explore the role of proximity-induced odd-frequency pairing in the thermoelectricity of a ferromagnet when coupled to a conventional $s$-wave spin-singlet superconductor through a spin-active interface. By varying both the polarization and its direction in the ferromagnet and the interfacial spin-orbit interaction strength, we analyze the behavior of all proximity-induced pair amplitudes in the ferromagnet and their contributions to the thermoelectric coefficients. Based on our results for the Seebeck coefficient, we predict that odd-frequency spin-triplet Cooper pairs are much more efficient than the conventional spin-singlet even-frequency pairs in enhancing thermoelectricity of the junction, and especially mixed-spin triplet pairing is favorable. Our results on the thermoelectric figure of merit show that ferromagnet/superconductor junctions are very good thermoelectric systems when superconductivity is dominated by odd-frequency pairing.