Hopf term and the effective Lagrangian for the Skyrmions in a two-dimensional electron gas at small g-factor

Abstract

We study interacting electrons in two dimensions moving in the lowest Landau level under the condition that the Zeeman energy is much smaller than the Coulomb energy and the filling factor is one. In this case, Skyrmion quasiparticles play an important role. Here, we present a simple and transparent derivation of the corresponding effective Lagrangian. In its kinetic part, we find a non-zero Hopf term the prefactor of which we determine rigorously. In the Hamiltonian part, we calculate, by means of a gradient expansion, the Skyrmion-Skyrmion interaction completely up to fourth order in spatial derivatives.

4 pages, Latex

References in corpus (6)

• Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions
• Evidence for Skyrmions and Single Spin Flips in the Integer Quantized Hall Effect
• 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
• Continuum quantum ferromagnets at finite temperature and the Quantum Hall effect
• Thermodynamics of Quantum Hall Ferromagnets

Cited by in corpus (14)

• Effective Field Theory Approach to Ferromagnets and Antiferromagnets in Crystaline Solids
• Hopf Term for a Two-Dimensional Electron Gas
• Lowest Landau level bosonization
• Spin relaxation in quantum Hall systems
• Quantum Mechanically Induced Hopf Term in the O(3) Nonlinear Sigma Model
• Bulk and edge excitations of a $\nu =1$ Hall ferromagnet
• Hopf invariant for long-wavelength skyrmions in quantum Hall systems for integer and fractional fillings
• Quantum Hall Ferromagnets: Induced Topological term and electromagnetic interactions
• Hopf Term, Fractional Spin and Soliton Operators in the O(3) Nonlinear Sigma Model
• Large and exact quantum degeneracy in a Skyrmion magnet
• Massive Spin Collective Mode in Quantum Hall Ferromagnet
• Electronic correlation in the quantum Hall regime
• Bag Formation in Quantum Hall Ferromagnets
• Hopf symmetry protected topological phases in the vicinity of spin orders