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Paper   IPM / P / 6593
School of Physics
  Title:   Field Theory of Skyrme Lattices in Quantum Hall Ferromagnets
1.  M. Abolfath
2.  M.R. Ejtehadi
  Status:   Published
  Journal: Phys. Rev. B
  No.:  48
  Vol.:  58
  Year:  1998
  Pages:   10665-10673
  Supported by:  IPM
We report the application of the nonlinear σ 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 ν = 1 where skyrmions are extremely dilute and a continuous transition into antiferromagnet square lattice occurs by increasing the skyrmion density and therefore [ν−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 superconductor-insulator and the non-zero temperature phase transitions.

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