Effect of Quenched Disorder in the Entropy-Jump at the First-Order Vortex Phase Transition of Bi$$_{}$$Sr$$_{}$$CaCu$$_{}$$O$$_{8 + \delta }$$8+δ

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 \(B_{\Phi }\)). In contrast with previous magneto-optical reports, we find that the first-order phase transition persists for samples with \(B_{\Phi }\) 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.