Skyrmion lattice melting in the quantum Hall system

Carsten Timm, S. M. Girvin, and H. A. Fertig
Phys. Rev. B 58, 10634 – Published 15 October 1998
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Abstract

The melting and magnetic disordering of the Skyrmion lattice in the quantum Hall system at filling factor ν1 are studied. A Berezinskii-Kosterlitz-Thouless renormalization-group theory is employed to describe the coupled magnetic and translational degrees of freedom. The nontrivial magnetic properties of the Skyrmion system stem from the in-plane components of the noncollinear magnetization in the vicinity of Skyrmions, which are described by an antiferromagnetic XY model. In a Coulomb gas formulation the “particles” are the topological defects of the XY model (vortices) and of the lattice (dislocations and disclinations). The latter frustrate the antiferromagnetic order and acquire fractional vorticity in order to minimize their energy. We find a number of melting/disordering scenarios for various lattice types. While these results do not depend on a particular model, we also consider a simple classical model for the Skyrmion system. It results in a rich T=0 phase diagram. We propose that the triangular and square Skyrmion lattices are generically separated by a centered rectangular phase in the quantum Hall system.

  • Received 6 April 1998

DOI:https://doi.org/10.1103/PhysRevB.58.10634

©1998 American Physical Society

Authors & Affiliations

Carsten Timm* and S. M. Girvin

  • Department of Physics, Indiana University, Bloomington, Indiana 47405

H. A. Fertig

  • Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506

  • *Present address: Freie Universität Berlin, Fachbereich Physik, Arnimallee 14, D-14195 Berlin, Germany.

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Vol. 58, Iss. 16 — 15 October 1998

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