Influence of force-free current on vortex lattice melting transition

The elastic free energy of the vortex lattice in the presence of the current distributed periodically in space, flowing parallel to the unperturbed vortex array, has been derived. The interaction of the vortex lattice phonons, having different wave vectors, occurs even in the elastic approximation due to the umklapp processes involving the reciprocal lattice vectors of the spatial Fourier transformation of the force-free current distribution. The mean square displacement of vortices from their equilibrium position is calculated for the case of the small non-homogeneous force-free current.