Skyrmions in the Quantum Hall Effect at Finite Zeeman Coupling

Using a self-consistent approximation for the spin distribution of Skyrmions in the quantum Hall effect, we obtain an effective action for the Skyrmion coordinates. The energy functional is minimized for a periodic distribution of Skyrmions with an underlying hexagonal symmetry. We calculate the phonon spectrum of this lattice and find that near the classical minimum, breathing modes of the Skyrmions are strongly suppressed. The resulting equal-sized Skyrmions interact via a residual Coulomb potential. Neglecting coupling between phonons and spin waves due to dipole and higher-order Coulomb interactions, the Skyrmion crystal has a phonon spectrum identical to that of an electronic Wigner crystal. The transition to a liquid of equal-sized Skyrmions is discussed using the theory of dislocation melting and a comparison is made between the predictions of this theory and the results of a recent experiment.