Numerical studies of the phase diagram of layered type-II superconductors in a magnetic field

Abstract

We report on simulations of layered superconductors using the Lawrence-Doniach model in the framework of the lowest-Landau-level approximation. We find a first-order phase transition with a $B(T)$ dependence which agrees very well with the experimental ``melting'' line in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.$ The transition is not associated with vortex lattice melting, but separates two vortex liquid states characterized by different degrees of short-range crystalline order and different length scales of correlations between vortices in different layers. The transition line ends at a critical end point at low fields. We find the magnetization discontinuity and the location of the lower critical magnetic field to be in good agreement with experiments in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}.$ Length scales of order parameter correlations parallel and perpendicular to the magnetic field increase exponentially as $1/T$ at low temperatures. The dominant relaxation time scales grow roughly exponentially with these correlation lengths. The consistency of our numerical results with various experimental features in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}},$ including the dependence on anisotropy, and the temperature dependence of the structure factor at the Bragg peaks in neutron scattering experiments is demonstrated.