Persistence of the first-order transition lines in mesoscopic Bi$_2$Sr$_2$CaCu$_2$O$_8$ vortex matter with less than hundred vortices

TL;DR

This study demonstrates that the first-order vortex matter transition line in mesoscopic Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ remains unchanged in size but surface effects influence the irreversible vortex region.

Contribution

It shows that the first-order transition line persists in systems with fewer than a hundred vortices, using sensitive AC magnetization techniques.

Findings

First-order transition line persists in small vortex systems.

Sample size reduction does not alter the transition line location.

Surface effects enlarge the irreversible vortex region.

Abstract

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.