Elasticity and melting of vortex crystals in anisotropic superconductors: Beyond the continuum regime

The elastic moduli of vortex crystals in anisotropic superconductors are fr equently involved in the investigation of their phase diagram and transport properties. We provide a detailed analysis of the harmonic eigen: values ( normal modes) of the vortex Lattice for general values of the magnetic fiel d strength, going beyond the elastic continuum regime. The detailed behavio r of these wave-vector-dependent eigenvalues within the Brillouin zone (BZ) . is compared with several frequently used approximations that we also reca lculate, Throughout the BZ, transverse modes are less costly than their lon gitudinal counterparts, and there is an angular dependence which becomes mo re marked close to the zone boundary. Based on these results, we propose an analytic correction to the nonlocal continuum formulas which Bts quite wel l the numerical behavior of the eigenvalues in the tendon regime. We use th is approximate expression to calculate thermal Fluctuations and the full me lting line (according to Lindeman's criterion) for various values of the an isotropy parameter.