First order melting of vortex lattice in strongly type-II three dimensional superconductors

We calculate the transition line of the first-order melting of vortex lattice in a three-dimensional type-II superconductor in fields of several Tesla, using the results from the density-functional theory of vortex melting in two-dimensions and a self-consistent Hartree treatment of correlations along the field. The result is in quantitative agreement with experiment. The temperature width of the hysteresis, the latent heat, the Debye-Waller factor and the magnetization at the transition are discussed. PACS numbers: 74.60.Ge Several recent experimental studies focused on the superconducting transition in untwinned YBCO samples in fields of several tesla [1, 2, 3, 4]. In contrast to earlier experiments in samples where the physics of the transition was dominated by inhomogeneities and where the transition appeared to be second order, the observed sharp hysteretic drop in resistivity in these very clean, strongly type-II materials in moderate magnetic fields suggests that the true vortex melting transition might be first order. This is somewhat surprising when one recalls that the mean-field Abrikosov theory predicts a second order phase transition for a homogeneous type-II superconductor in magnetic field. Thus here one encounters another possible example of strong thermal fluctuations changing the order of transition. An early suggestion that this might happen in a type-II superconductor in vicinity of Hc2(T ) came from the renormalization group analysis [5] close to the upper critical dimension dup = 6, as well as from the analysis of the theory with infinite number of order parameter components in 4 < d < 6 [6]. This is inadequate however for the physical three-dimensional (3D) samples which are below the lower critical dimension dlow = 4 in the problem considered there. Usually, the transition in the vortex system is described by the harmonic theory of vortex lattice and by invoking phenomenological Lindemman criterion to locate the melting point [7, 8]. This is however a suspect starting point if one is interested in describing strong fluctuations near Hc2(T ) and is more appropriate for the low-field or T ≈ 0 region of the phase diagram. As emphasized by Moore [9], in this description one starts from the Abrikosov lattice solution for the order parameter which is unstable with respect to harmonic shear modes of the lattice at any finite temperature in two and three dimensions. It is therefore inconsistent to simply assume this ordered low-temperature state. Furthermore, the numerical constant in Lindemman criterion needs to be chosen phenomenologically, and the requisite number can actually differ by orders of magnitude from one material to another [10]. Recently, a novel approach to the problem has been formulated that encompasses the difficulties mentioned above by relying on a new physical picture of the phase transition in