The elasticity theory for the vortex lattice is of the form
where , , and are the bulk, shear, and tilt moduli, respectively. In two dimensions, the appropriate Hamiltonian is obtained by simply dropping all from Eq. 145. At small wavevectors, , these become constant, but, more generally,
The shear modulus is essentially wave-vector dependent.
Even this level of complexity is not quite realistic for the anisotropic layered materials of most experimental relevance. We shall not much consider these extensions, which are outside of the scope of this course. One should, however, keep in mind the non-trivial difficulties in making a direct and quantitative comparison with experiments.