Vortices and 2D Bosons: A Path-Integral Monte Carlo Study

Abstract

The vortex system in a high- ${T}_{c}$ superconductor has been studied numerically using the mapping to 2D bosons and the path-integral Monte Carlo method. We find a single first-order transition from an Abrikosov lattice to an entangled vortex liquid. The transition is characterized by an entropy jump $\ensuremath{\Delta}S\ensuremath{\approx}{0.4k}_{B}$ per vortex and layer (parameters for ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$) and a Lindemann number ${c}_{L}\ensuremath{\approx}0.25$. The increase in density at melting is given by $\ensuremath{\Delta}\ensuremath{\rho}\ensuremath{\approx}6.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}/\ensuremath{\lambda}(T{)}^{2}$. The vortex liquid corresponds to a bosonic superfluid, with ${\ensuremath{\rho}}_{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\rho}$ even in the limit $\ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$.