Elastic moduli of vortex lattices within nonlocal London model

Vortex lattice (VL) elastic response is analyzed within nonlocal London model. The squash modulus turns zero at the field $H_{\Box}$ where VL undergoes square-to-rhombus structural transition. In the field region $H>H_{\Box}$ where the square VL is stable, the rotation modulus turns zero at a field $H_r$ indicating instability of the square VL with respect to rotations. The shear modulus depends on the shear direction; the dependence is strong in the vicinity of $H_{\Box}$ where the square VL is soft with respect to the shear along [110]. The $H$ dependences of elastic moduli are evaluated for LuNi$_2$B$_2$C.