Instabilities in the flux-line lattice of anisotropic superconductors

Abstract

The stability of the flux-line lattice has been investigated within anisotropic London theory. This is a full-scale investigation of instabilities in the ``chain'' state, the equilibrium lattice that is similar to the Abrikosov lattice at large fields but crosses over smoothly to a pinstripe structure at low fields. By calculating the normal modes of the elasticity matrix, it has been found the lattice is stable at large fields, but that instabilities occur as the field is reduced. The field at which these instabilities first arise, ${\mathrm{b}}^{\mathrm{*}}$(\ensuremath{\epsilon},\ensuremath{\theta}), depends on the anisotropy \ensuremath{\epsilon} and the angle \ensuremath{\theta} at which the lattice is tilted away from the c axis. These instabilities initially occur at wave vector ${\mathbf{k}}^{\mathrm{*}}$(\ensuremath{\epsilon},\ensuremath{\theta}). The dependence of ${\mathbf{k}}^{\mathrm{*}}$ on \ensuremath{\epsilon} and \ensuremath{\theta} is complicated, but the component of ${\mathbf{k}}^{\mathrm{*}}$ along the average direction of the flux lines, ${\mathrm{k}}_{\mathrm{z}}$, is always finite. For rigid straight flux lines, the cutoff necessary for London theory has been ``derived'' from Landau-Ginzburg theory, where the shape of the vortex core is known. However, for investigating instability at finite ${\mathrm{k}}_{\mathrm{z}}$ it is necessary to know the dependence of the cutoff on ${\mathrm{k}}_{\mathrm{z}}$, and we have used a cutoff suggested by Sudb\o{} and Brandt. The instabilities only occur for values of the anisotropy \ensuremath{\epsilon} appropriate to a material like BSCCO, and not for anisotropies more appropriate to YBCO. The lower critical field ${\mathrm{H}}_{\mathrm{c}1}$(\ensuremath{\varphi}) is calculated as a function of the angle \ensuremath{\varphi} at which the applied field is tilted away from the crystal axis. The presence of kinks in ${\mathrm{H}}_{\mathrm{c}1}$(\ensuremath{\varphi}) is seen to be related to instabilities in the equilibrium flux-line structure.