Field Theory of Skyrme Lattices in Quantum Hall Ferromagnets

Abstract

We report the application of the nonlinear $\sigma$ model to study the multi-skyrmion problem in the quantum Hall ferromagnet system. We make use of a first-principle calculation to derive an analytical form for the inter-skyrmionic interaction to show that the ground state of the system can be described by a ferromagnet triangular Skyrme lattice near $\nu =1$ where skyrmions are extremely dilute and a continuous transition into antiferromagnet square lattice occurs by increasing the skyrmion density and therefore $|\nu -1|$. Using these results we demonstrate that the transition for a triangular to a square lattice which was previously derived, using the Hartree-Fock method, can also be seen in the field theory picture. We investigate the possibility that the skyrmions bound in pair to make a bi-skyrmion triangular lattice when the Zeeman energy is extremely small. We show that the energy of a skyrmion with charge $Q$ is less than the energy of $Q$ skyrmions each with charge one when the short range interaction among them is considered. By taking the quantum fluctuations into account, we also argue the possibility of the existence of a %SMG superconductor-insulator and the non-zero temperature phase transitions.

Accepted for publication in Phys. Rev. B

References in corpus (5)

• Collective Excitations, NMR, and Phase Transitions in Skyrme Crystals
• A critical comparison of classical field theory and microscopic wavefunctions for skyrmions in quantum Hall ferromagnets
• Quantum Hall Skyrmions with Higher Topological Charge
• Shape Deformation driven Structural Transitions in Quantum Hall Skyrmions
• Quantum fluctuations of classical skyrmions in quantum Hall Ferromagnets

Cited by in corpus (2)

• Pinning mode resonance of a Skyrme crystal near Landau level filling factor $\nu$=1
• Towards a phase diagram of the 2D Skyrme model