Skyrmions in the quantum Hall effect at finite Zeeman coupling

Abstract

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 minimised for a periodic distribution of Skyrmions with an underlying hexagonal symetry. 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.

17 pages, LaTex, 4 Postscript figures

References in corpus (5)

• Evidence of Skyrmion excitations about $\nu =1$ in n-Modulation Doped Single Quantum Wells by Inter-band Optical Transmission
• Skyrme Crystal In A Two-Dimensional Electron Gas
• Giant Low Temperature Heat Capacity of GaAs Quantum Wells near Landau Level Filling $\nu$=1
• Skyrmions without Sigma Models in Quantum Hall Ferromagnets
• Skyrmion Liquid in SU(2)-invariant Quantum Hall Systems

Cited by in corpus (10)

• Spin waves in a skyrmion crystal
• Coreless and singular vortex lattices in rotating spinor Bose-Einstein condensates
• Microwave Resonance of 2D Wigner Crystal around integer Landau fillings
• Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization
• Pinning mode resonance of a Skyrme crystal near Landau level filling factor $\nu$=1
• Enhancement of the $\nu =5/2$ Fractional Quantum Hall State in a Small In-Plane Magnetic Field
• Multicomponent Skyrmion lattices and their excitations
• Optics with Quantum Hall Skyrmions
• Thermal Activation Signatures of the Anderson Insulator and the Wigner Solid forming near $\nu =1$
• Disorder Enhanced Nuclear Spin Relaxation at Landau Level Filling Factor One