Finite-size effects and anisotropic melting of the vortex solid in high-temperature superconductors

Abstract

A mean-field model of anisotropic melting of the vortex solid in high-temperature superconductors is proposed. For a slab sample with dimensions ${\mathit{l}}_{\mathit{a}\mathit{b}}$≫${\mathit{l}}_{\mathit{c}}$, where 2${\mathit{l}}_{\mathit{a}\mathit{b}}$ and 2${\mathit{l}}_{\mathit{c}}$ are the average diameter of the ab plane and the c axis thickness, respectively, large thermal fluctuations and finite-size effects may result in anisotropic two-dimensional melting at crossover temperatures ${\mathit{T}}_{\mathit{X}}$(H) below the three-dimensional-melting transition ${\mathit{T}}_{\mathit{M}}$(H). Thus a quasi-two-dimensionally ordered vortex-liquid phase may exist in ${\mathit{T}}_{\mathit{X}}$(H) <T<${\mathit{T}}_{\mathit{M}}$(H). Generally, ${\mathit{T}}_{\mathit{X}}$(H) decreases with the decreasing sample thickness, increasing magnetic field, and larger Ginzburg-Landau parameter κ(==λ/ξ). In the limit of 1/2${\mathit{H}}_{\mathit{c}2}$≪H<${\mathit{H}}_{\mathit{c}2}$, the geometric anisotropy plays a more important role in determining ${\mathit{T}}_{\mathit{X}}$(H) than the electronic-mass anisotropy.