Mixed pairing symmetries and flux-induced spin current in mesoscopic superconducting loops with spin correlations

Abstract

We numerically investigate the mixed pairing symmetries in mesoscopic superconducting loops in the presence of spin correlations by solving the Bogoliubov-de Gennes equations self-consistently. The spatial variations of the superconducting order parameters and the spontaneous magnetization are determined by the band structure. When the threaded magnetic flux turns on, the charge and spin currents both emerge and depict periodic evolution. In the case of a mesoscopic loop with dominant triplet ${p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}$-wave symmetry, a slight change of the chemical potential may lead to novel flux-dependent evolution patterns of the ground-state energy and the magnetization. The spin-polarized currents show pronounced quantum oscillations with fractional periods due to the appearance of energy jumps in flux, accompanied with a steplike feature of the enhanced spin current. Particularly, at some appropriate flux, the peaks of the zero-energy local density of states clearly indicate the occurrence of the odd-frequency pairing. In the case of a superconducting loop with dominant singlet ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave symmetry, the spatial profiles of the zero-energy local density of states and the magnetization show spin-dependent features on different sample diagonals. Moreover, the evolution of the flux-induced spin current always exhibits an $hc/e$ periodicity.