Calculation of the shear modulus of a two-dimensional vortex lattice

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Abstract
We have calculated the temperature-dependent shear modulus μ(T) of a vortex lattice in a two-dimensional superconductor. We include fluctuations by expanding the Ginzburg-Landau free-energy functional in states from the lowest Landau level, and evaluate the shear modulus by standard Monte Carlo techniques for rectangular samples containing up to 224 vortices. At the thermodynamic melting transition, which is apparently first order as found by previous workers, the shear modulus falls from a finite value in the solid phase to zero in the liquid. Despite the first-order transition, the magnitude of the drop may be near the universal value envisioned in dislocation-unbinding theories.