The threshold temperature where type-I and type-II interchange in mesoscopic superconductors at the Bogomolnyi limit

Abstract In this work we discuss the H − T phase diagram for mesoscopic squared superconducting samples at the Bogomolnyi limit, where the Ginzburg–Landau constant κ = 1 / 2 . We calculate H p ( T ) , the vortex penetration field, and H u ( T ) the upper critical field. Through the study of the temperature dependence on the H p , it is possible to distinguish the region where the magnetic field penetrates into the sample, like a type-I or a type-II superconductor. It permits to determine the threshold temperature T ⋆ ( L , H ) where the phase transition from type-I to type-II occurs for some different sizes L of the mesoscopic superconducting samples. The calculation of the upper critical field H u ( T ) , for these samples, shows that, these two curves, H p ( T ) and H u ( T ) , overlap at the threshold temperature mentioned above. The magnetization of the system was calculated for all sizes studied in this work, and for temperatures above and below T ⋆ ( L , H ) . This study confirms the existence of the threshold temperature, T ⋆ ( L , H ) , where type-I and type-II interchange in mesoscopic superconductors at the Bogomolnyi limit.