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The persistence of the first-order transition line in the phase diagram of mesoscopic Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ vortex matter is detected down to a system size of less than hundred vortices. Precise and highly-sensitive to bulk currents AC magnetization techniques proved to be mandatory in order to obtain this information. The location of the vortex matter first-order transition lines are not altered by decreasing the sample size down to 20 $mu$m. Nevertheless, the onset of irreversible magnetization is affected by increasing the sample surface-to-volume ratio producing a noticeable enlargement of the irreversible vortex region above the second-peak transition.
The thermodynamic $H-T$ phase diagram of Bi$_2$Sr$_2$CaCu$_2$O$_8$ was mapped by measuring local emph{equilibrium} magnetization $M(H,T)$ in presence of vortex `shaking. Two equally sharp first-order magnetization steps are revealed in a single tempe
Vortex phase diagram under tilted fields from the $c$ axis in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+y}$ is studied by local magnetization hysteresis measurements using Hall probes. When the field is applied at large angles from the $c$ axis, an anomaly (
Langevin dynamics simulations of the vortex matter in the highly-anisotropic high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ were performed. We introduced point defects as a smoothened distribution of a random potential. Both the electromag
Low temperature thermal conductivity, $kappa$, of optimally-doped Bi2212 was studied before and after the introduction of point defects by electron irradiation. The amplitude of the linear component of $kappa$ remains unchanged, confirming the univer
A magnetic field applied to type-II superconductors introduces quantized vortices that locally quench superconductivity, providing a unique opportunity to investigate electronic orders that may compete with superconductivity. This is especially true