Probing superconductivity in MgB2 confined to magnetic field tuned cylinders by means of critical fluctuations

We report and analyze reversible magnetization measurements on a high quality MgB2 single crystal in the vicinity of the zero field transition temperature, T_c=38.83 K, at several magnetic fields up to 300 Oe, applied along the c-axis. Though MgB2 is a two gap superconductor our scaling analysis uncovers remarkable consistency with 3D-xy critical behavior, revealing that close to criticality the order parameter is a single complex scalar as in 4He. This opens up the window onto the exploration of the magnetic field induced finite size effect, whereupon the correlation length transverse to the applied magnetic field H_i applied along the i-axis cannot grow beyond the limiting magnetic length L_Hi, related to the average distance between vortex lines. We find unambiguous evidence for this finite size effect. It implies that in type II superconductors, such as MgB2, there is the 3D to 1D crossover line H_pi and xi denotes the critical amplitudes of the correlation lengths above and below T_c along the respective axis. Consequently, above H_pi(T) and T<T_c superconductivity is confined to cylinders with diameter L_Hi (1D). In contrast, above T_c the uncondensed pairs are confined to cylinders. Accordingly, there is no continuous phase transition in the (H,T)-plane along the H_c2-lines as predicted by the mean-field treatment.