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Vortex lattices

The elasticity theory for the vortex lattice is of the form


where tex2html_wrap_inline3450 , tex2html_wrap_inline3452 , and tex2html_wrap_inline3454 are the bulk, shear, and tilt moduli, respectively. In two dimensions, the appropriate Hamiltonian is obtained by simply dropping all tex2html_wrap_inline3456 from Eq. 145. At small wavevectors, tex2html_wrap_inline3458 , these become constant, but, more generally,


The shear modulus tex2html_wrap_inline3460 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.

Leon Balents
Thu May 30 08:21:44 PDT 1996