We systematically measure the superconducting (SC) and mixed state properties of high-quality CsV3Sb5 single crystals with Tc ~ 3.5 K. We find that the upper critical field Hc2(T) exhibits a large anisotropic ratio of Hc2^(ab)/Hc2^(c) ~ 9 at zero temperature and fitting its temperature dependence requires a minimum two-band effective model. Moreover, the ratio of the lower critical field, Hc1^(ab)/Hc1^(c), is also found to be larger than 1, which indicates that the in-plane energy dispersion is strongly renormalized near Fermi energy. Both Hc1(T) and SC diamagnetic signal are found to change little initially below Tc ~ 3.5 K and then to increase abruptly upon cooling to a characteristic temperature of ~2.8 K. Furthermore, we identify a two-fold anisotropy of in-plane angular-dependent magnetoresistance in the mixed state. Interestingly, we find that, below the same characteristic T ~ 2.8 K, the orientation of this two-fold anisotropy displays a peculiar twist by an angle of 60o characteristic of the Kagome geometry. Our results suggest an intriguing superconducting state emerging in the complex environment of Kagome lattice, which, at least, is partially driven by electron-electron correlation.
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