Defect induced melting of vortices in high-${\bf T_c}$ 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 ${\rm YBa}_2 {\rm Cu}_3 {\rm O}_{7-δ}$, and with modifications also for ${\rm Bi}_2 {\rm Sr}_2 {\rm Ca} {\rm Cu}_2 {\rm O}_8$ . We calculate the jumps in the entropy and the magnetic induction at the melting transition.

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