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Electronic structure and spin-lattice relaxation in superconducting vortex states on the kagome lattice near van Hove filling

Starting from a tight-binding model on the kagome lattice near the van Hove filling, the superconducting (SC) properties are investigated self-consistently using the Bogoliubov-de Gennes equation with the consideration of the inequivalent third-neighbor (TN) bonds. Near the van Hove filling, the most favorable SC pairings are found to derive from the electrons belonging to the same sublattice sites, including the on-site $s$-wave and the spin-singlet/triplet TN pairings. The inequivalent TN bonds will result in multiple SC components with different orbital angular momentums (OAM) for the TN SC pairings. While the density of states (DOS) and the temperature ($T$) dependence of the spin-lattice relaxation rate ($T^{-1}_{1}$) exhibit distinct line shapes in the SC state for the three cases, a peak structure in the $T$ dependence of $T^{-1}_{1}$ can be found for both cases just below $T_{c}$ as a result of the van Hove singularity, even though the SC gap has nodes. The effects of magnetic vortices on the low energy excitations and on the $T$ dependence of $T^{-1}_{1}$ with the implications of the results are also discussed for both cases.