Electric field-induced nonreciprocal spin current due to chiral phonons in chiral-structure superconductors

A recent experiment [Nakajima, et al., Nature 613, 479 (2023)] has reported a pair of oppositely polarized spins under an alternating electric current in a superconductor with a chiral structure. However, these behaviors cannot be explained by the conventional Edelstein effect and require a new mechanism. In this Letter, we propose a mechanism of spin current generation under an external electric field due to chiral phonons in a chiral-structure superconductor based on the Bogoliubov de Gennes and the Boltzmann equations. In our mechanism, chiral phonons are induced by electric field due to inversion symmetry breaking and electron–phonon interaction. They work as an effective Zeeman field and hence spin-polarize Bogoliubov quasiparticles in the superconductor. As a result, the spin current carried by the quasiparticles flows along the screw axis and shows a quadratic dependence on the electric field at the low-field range, leading to a nonreciprocal spin transport. The spin current also shows a nonmonotonic temperature dependence, reaching its maximum at around the superconducting transition temperature.