Spin-Nernst Effect and Spin-Seebeck Effect in Time-Reversal Invariant Topological Superconductors and Non-Unitary Superconductors

The existence of spin-triplet Cooper pairs is a key ingredient offering pathways to exotic superconductivity, including topological and non-unitary superconducting states. The realization of these states relies on spin-orbital coupling, which determines the relationship between the spin and momentum of the Cooper pairs in the condensate. For example, spin-chirality of the triplet pairs has been established as the most promising route to realize non-trivial topology in time-reversal invariant superconductors. Non-unitary triplet Cooper pairs with net spin magnetization are implicated in many theories of the interplay of superconductivity and magnetism, including in ferromagnetic (or nearly ferromagnetic) superconductors. However, there are few direct experimental probes of spin chirality and Cooper pair spin magnetization. In this talk, we propose such probes, showing that the spin-Nernst effect and the spin-Seebeck effect are directly related to the spin chirality and net spin moment of the Cooper pairs respectively. Therefore, measurements of these transport coefficients can identify time-reversal invariant topological and non-unitary superconductors.