Effect of quenched disorder in the entropy-jump at the first-order vortex phase transition of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$

We study the effect of quenched disorder in the thermodynamic magnitudes entailed in the first-order vortex phase transition of the extremely layered Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ compound. We track the temperature-evolution of the enthalpy and the entropy-jump at the vortex solidification transition by means of AC local magnetic measurements. Quenched disorder is introduced to the pristine samples by means of heavy-ion irradiation with Pb and Xe producing a random columnar-track pins distribution with different densities (matching field $B_{\mathrm{\Phi }}$). In contrast with previous magneto-optical reports, we find that the first-order phase transition persists for samples with $B_{\mathrm{\Phi }}$ up to 100,Gauss. For very low densities of quenched disorder (pristine samples), the evolution of the thermodynamic properties can be satisfactorily explained considering a negligible effect of pinning and only electromagnetic coupling between pancake vortices lying in adjacent CuO planes. This description is not satisfactory on increasing magnitude of quenched disorder.