dHvA effect and superconductivity of MgB2 detected by AC torque method down to the fields below Hc2

We have grown high quality single crystals of MgB2 by the encapsulation method. A new method which combines the magnetic torque method and the field modulation method is successfully employed to detect the dHvA oscillation and the AC response of the superconductor down to the fields below Hc2. The AC torque signal indicates that the surface superconductivity develops well above Hc2 and it evolves into the bulk superconductivity with decreasing field. The irreversible torque curve is observed at much higher fields than Hc2 and can be attributed to a pinning effect of the surface vortices. The superconducting transition detected by the AC torque method significantly broadens indicating that the supercondcuting fluctuation is not negligible. It is suggested that both the surface superconductivity and the fluctuation contribute considerably to the broadening of the resistive transition. We have found that the damping of the dHvA signal from the π band is very large around Hc2 due to the superconducting fluctuation and the pinning effect, but the damping rate becomes moderate with further decreasing field, implying that the superconducting gap may be small for the π band near Hc2.