Linear response and instability of vortex lattice in type-II superconductors

The wave vector dependent linear response of the vortex lattice in type-II superconductors is studied by calculating the superfluid density and is shown to have a singular behavior with respect to the long wave length perturbation of vector potential. The calculations are carried out in terms of the nonlinear elastic theory of the vortex lattice, which is, in principle, a low temperature expansion, and the terms up to the first order in temperature are taken into account, which is beyond the usual Gaussian elastic theory. The superfluid density is found to behave as ~ k_BT ¦k¦² log ¦k¦,for the small wave vector,k,perpendicular to the external magnetic field, where Tand k_B are the temperature and the Boltzmann constant, respectively. This behavior causes the divergence of the magnetic susceptibility at a critical wave vector, k_c.We show that this behavior is associated with an instability of vortex lattice to the externally applied perturbation.