Abstract
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 efficient than the conventional spin-singlet even-frequency pairs in enhancing thermoelectricity of the junction, 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.
Highlights
The phenomenon of odd-frequency superconductivity occurs when the superconducting pair expectation value is odd under the exchange of time, or equivalently frequency, of the two electrons in the Cooper pair [1,2,3,4]
Is thermoelectricity in FM/SC junctions enhanced in the presence of odd-ω pairing compared to the scenario when there is only even-ω pairing in the system? Or, in other words, how efficient are oddω Cooper pairs as carriers of the thermoelectric current to make the FM/SC junction an efficient thermoelectric system? the existence of a finite density of states within the SC gap due to odd-ω superconductivity [49,50] is interesting, as that might influence the subgap contributions to the thermal current, which is absent in the case of even-ω pairing
Having developed the necessary theoretical framework, we present our results of the Seebeck coefficient and thermoelectric figure of merit for FM/SC junction and discuss the role of the proximity-induced pair amplitude
Summary
The phenomenon of odd-frequency (odd-ω) superconductivity occurs when the superconducting pair expectation value is odd under the exchange of time, or equivalently frequency, of the two electrons in the Cooper pair [1,2,3,4]. Recently Keidel et al, have proposed a way to generate equal-spin triplet Cooper pairs at the helical edge states of a quantum spin Hall insulator and used that to drive a supercurrent from a temperature gradient in a SC/FM insulator/SC structure along the edge [48] Despite these interesting results, it is not yet established whether odd-ω pairing is a good carrier of thermoelectricity in generic FM/SC structures. Enhancement of the Seebeck coefficient indicates the possibility of getting good thermopower based on odd-ω superconductivity This prediction is supported by our result of the thermoelectric figure of merit zT , characterizing the efficiency of the junction. We our results set are valid for any T /Tc < 1 including the experimentally accessible temperatures Our system size for the FM/SC junction is sufficiently large as the SC coherence length is 10a with a being the lattice constant
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