Nonlocal elastic properties of flux-line lattices in anisotropic superconductors in an arbitrarily oriented field

The real-space anisotropic interaction between arbitrarily curved London vortices is calculated for a uniaxially anisotropic superconductor. From this we derive the elastic energy of a distorted flux-line lattice (FLL) in a uniaxially anisotropic superconductor for inductions B≪${\mathit{B}}_{\mathit{c}2}$ and arbitrary field direction. Avoiding the continuum description of the FLL, we obtain the exact elastic matrix, which is periodic in Fourier space and from which all elastic moduli of the FLL may be extracted. In the continuum limit, we give explicit expressions for the various nonlocal tilt and bulk moduli for the two cases B⊥c^ and B?c^; here c^ is the symmetry axis of the uniaxial crystal perpendicular to the basal plane. These results complement previous local theories and extend previous nonlocal treatments.