Defect induced melting of vortices in high-${\mathbf{T}}_{\mathbf{c}}$ superconductors: A model based on continuum elasticity theory

We set up a melting model for vortex lattices in high-temperature superconductors based on the continuum elasticity theory. The model is Gaussian and includes defect fluctuations by means of a discrete-valued vortex gauge field. We derive the melting temperature of the lattice and predict the size of the Lindemann number. Our result agrees well with experiments for $ {\rm YBa}_2 {\rm Cu}3 {\rm O}{7-\delta} $,andwithmodificationsalsofor$ {\rm Bi}_2 {\rm Sr}_2 {\rm Ca} {\rm Cu}_2 {\rm O}_8 $ . We calculate the jumps in the entropy and the magnetic induction at the melting transition.