Vortex Matter in nano-structured superconductors

We have fabricated anti-dots array in Nb and NbN, and high-Tc superconductor Bi-2212 with the diameter of r and the spacing of a, and have measured the flow-resistance of vortices perpendicular to the array and magnetic field. Depending also to the ratio of r/a, we can produce a variety of vortex-matching effect; the usual and the fractional matching. In low-Tc superconductors, the usual matching effect shows ``dips'' in the flow resistance at the matching field. However, it shows ``humps'' at higher magnetic fields, which may be related to the formation of giant vortices and interstitial vortices, depending on the ratio r/a. The matching phenomena seem to occur just like the Bloch electrons in two-dimensional electron system with crystalline lattice under magnetic field. The anti-dot array acts as a crystalline lattice to the vortices. In this case, vortex flow-resistance corresponds to Tc in the linearlized GL equation. Generation and annihilation of the fractional matching effect might be well reproduced. In high-Tc superconductor, the matching effect is closely related to the first order vortex lattice melting of the pristine samples in the presence of the anti-dot arrays and with changing the potential energy of the vortex pinning.