Energy landscape and shear modulus of interlayer Josephson vortex   systems
  The ground state of interlayer Josephson vortex systems is investigated on the basis of a simplified Lawrence-Doniach model in which spatial dependence of the gauge field and the amplitude of superconducting order parameter is not taken into account. Energy landscape is drawn with respect to the in-plane field, the period of insulating layers including Josephson vortices, and the shift from the aligned vortex lattice. The energy landscape has a multi-valley structure and ground-state configurations correspond to bifurcation points of the valleys. In the high-field region, the shear modulus becomes independent of field and its anisotropy dependence is given by $c_{66}\propto \gamma^{-4}$. 
Yoshihiko Nonomura, Xiao Hu