Two-dimensional density-functional approach to the Abrikosov vortex lattice melting

Abstract

We present a theoretical study of the melting of the Abrikosov vortex lattice in the mixed state of high- Tc superconductors. We start from the Ginzburg-Landau theory which provides, in a wide region of the mixed state, the surface density of the vortex lattice in terms of the external magnetic field and the temperature. The interaction between vortex lines is modeled by means of a pairwise potential built up as a sum of a hard-core contribution plus a repulsive long-range tail. The free energy of the vortex system is evaluated by means of a density-functional theory which carries out a nonlocal treatment of the repulsive cores of the vortices. We present results for a Ginzburg-Landau susceptibility k572 as appropriate for YBa2Cu3O72y ~YBCO!. The competition between the entropic term due to excluded volume effects and the repulsive vortex-vortex interactions determines, in our model, the coexistence of both a solid and a fluid phase. The corresponding melting transition exhibits a reentrant behavior, in agreement with previous theoretical works and has a very weak first-order character. @S0163-1829~97!01738-4# I. INTRODUCTION The most outstanding property of the phase diagram of a type-II superconductor is the existence of two critical lines Hc1 (T) and Hc2 (T). When magnetic fields smaller than the lower critical field Hc 1 (T) are applied, the material presents a complete Meissner effect and the field penetrates it only in a region of thickness d(T) ~penetration length!. External fields larger than the upper critical fieldHc 2 (T) suppress the superconductivity and cause the transition to the normal state. In the region between these two lines the Meissner effect is incomplete and the field is able to penetrate the material in form of cylinders of flux, often referred to as vortices, inside which the superconductivity is suppressed. The number of vortices grows as the magnetic field is increased. This state, typical of type-II superconductors, is known as the mixed state. The vortices are parallel to the applied magnetic field and each one carries a flux quantum. The low-temperature phase of the vortex system is the Abrikosov lattice, 1 experimentally observed for both conventional 2 and high-Tc superconductors 3 in a wide region of the mixed state. The maintenance of superconducting properties in the mixed state is related to the presence of defects in the underlying material lattice. These defects may act as pinning centers and allow the supercurrents to flow around the vortices. The above phenomenology has been extensively studied, making use of Ginzburg-Landau ~GL! theory. 4,5 This theory predicts the presence of the Abrikosov vortex lattice up to the upper critical field and relates the disappearance of the superconductivity to the fact that, in the neighborhood of Hc 2 (T), vortices are so closely packed as to interpenetrate each other. However, thin films of conventional superconductors and high-T c layered superconductors present a rich phenomenology which does not correspond to this latter explanation. In particular, the presence of an additional line in the mixed state, the so-called irreversibility line, has been observed. 6‐8 The magnetic behavior of the material changes from reversible, below this line, to irreversible, above it. The origin of this line has been ascribed to the melting of the Abrikosov vortex lattice into different flux line fluid phases. 9,10 High-Tc superconductors present a combination of some properties that enhance the effects of thermal fluctuations leading to the lattice melting. Among them we underline high critical temperatures, short coherence lengths, large penetration depths, and quasi-two-dimensionality ~see Refs. 9‐11!. On the other hand, for thin films of conventional superconductors, the lattice melting is associated with the