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Skyrmions in Quantum Hall Systems

Under certain conditions, two-dimensional electron systems in strong magnetic field behave as ``quantum Hall ferromagnets''. These unusual ferromagnets have the novel property that the local magnetic vorticity (or ``Skyrmion'' density) is directly related to the physical charge density. In view of this vorticity/charge equivalence, electrical potentials couple directly to the magnetic vorticity.

Within the present context, a ``Skyrmion'' is a configuration of a two-dimensional ferromagnet which has a non-trivial global topological structure (this Skyrmion configuration cannot be deformed into the magnetic groundstate, in which all spins are aligned, by a smooth or continuous process). The importance of Skyrmions for quantum Hall systems arises from the discovery (based on both theoretical and experimental evidence) that they describe the lowest-energy charged excitations of quantum Hall ferromagnets, and therefore dominate many of the low-temperature properties of these systems.
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Schematic illustration of a Skyrmion in a two-dimensional ferromagnet. Many degenerate configurations can be generated by rotating all spins around a fixed axis.


Skyrmions in the Moore-Read state at nu=5/2
A. Wójs, G. Möller, S. H. Simon and N. R. Cooper
Phys. Rev. Lett. 104, 086801 (2010) [PRL, arXiv:0910.4176]

Dissipative Transport in Quantum Hall Ferromagnets by Spinwave Scattering
A. G. Green and N. R. Cooper
Phys. Rev. B 65, 125329 (2002) [PRB, cond-mat/0201095]

Large Skyrmions in an Al0.13Ga0.87As Quantum Well
S. P. Shukla, M. Shayegan, S. R. Parihar, S. A. Lyon, N. R. Cooper, and A. A. Kiselev
Phys. Rev. B 61, 4469 (2000) [PRB, cond-mat/9908452]

Solitary Waves in Planar Ferromagnets and the Breakdown of the Spin-Polarized Quantum Hall Effect
N. R. Cooper
Phys. Rev. Lett. 80, 4554 (1998) [PRL, cond-mat/9801160]

Excitonic recombination processes in Spin Polarised Two Dimensional Electron Gases
J. L. Osborne, A. J. Shields, M. Y. Simmons, N. R. Cooper, D. A. Ritchie, M. Pepper
Phys. Rev. B 58, R4227 (1998) [PRB]

Skyrmions in Quantum Hall Systems with Realistic Force-Laws
N. R. Cooper
Phys. Rev. B 55, R1934 (1997) [PRB, cond-mat/9611080]

Theory of Photoluminescence of the nu=1 Quantum Hall State: Excitons, Spin-waves and Spin-textures
N. R. Cooper and D. B. Chklovskii
Phys. Rev. B 55, 2436 (1997) [PRB, cond-mat/9607002].