A Parrinello–Rahman approach to vortex lattices

We present a framework for studying vortex lattice patterns and their structural transitions, using the Parrinello–Rahman (PR) method for molecular-dynamics (MD) simulations. Assuming an interaction between vortices derived from a Ginzburg–Landau field-theoretic context, we extract the ground-state of a "vortex gas" using the PR-MD technique and find it to be a triangular pattern. Other patterns are also obtained for special initial conditions. Generalizations of the technique, such as the inclusion of external potentials or excitation of quadrupolar modes, are also commented upon.