Ground state of interlayer Josephson vortex systems and the shear modulus

Ground state of interlayer Josephson vortex systems is investigated on the basis of the full Lawrence-Doniach model. We find: (1) For low fields, field dependence of $c_{66}$ approximately coincides with the elastic theory, and jumps in $c_{66}$ correspond to the structural phase transitions between various rotated-lattice configurations. (2) For intermediate fields, the ground state is characterized by continuously-varying shearing angle of vortex lattices. In this region $c_{66}$ becomes smaller than those in the elastic theory, and vanishes at the shear instability field. This critical field is increased by inhomogeneity of the magnetic field. (3) For high fields, $c_{66}$ converges to a constant value, which is quite different from the exponentially-decaying $c_{66}$ in the London theory. This saturation of $c_{66}$ can be interpreted as the effect of ``effective core size" within the elastic theory, and is not affected by inhomogeneity of the superconducting amplitude for material parameters of cuprate high-$T_{\rm c}$ superconductors.