Hamiltonian Theory of the Composite Fermion Wigner Crystal

Details Hamiltonian Theory of the Composite Fermion Wigner Crystal Hamiltonian Theory of the Composite Fermion Wigner Crystal

2001-04-30

arxiv.org/abs/cond-mat/0104579v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

41 page, 6 figures, 3 tables

Scientific paper

10.1103/PhysRevB.64.245326

Experimental results indicating the existence of the high magnetic field Wigner Crystal have been available for a number of years. While variational wavefunctions have demonstrated the instability of the Laughlin liquid to a Wigner Crystal at sufficiently small filling, calculations of the excitation gaps have been hampered by the strong correlations. Recently a new Hamiltonian formulation of the fractional quantum Hall problem has been developed. In this work we extend the Hamiltonian approach to include states of nonuniform density, and use it to compute the excitation gaps of the Wigner Crystal states. We find that the Wigner Crystal states near $\nu=1/5$ are quantitatively well described as crystals of Composite Fermions with four vortices attached. Predictions for gaps and the shear modulus of the crystal are presented, and found to be in reasonable agreement with experiments.

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