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Electron densities for the ground state of N=7 electrons in a magntic field, at: (a) fractional filling ν =1/3, corresponding to the angular momentum L2 = 63, shown in red on the left hand side (α = 0, β = 1). The total wave function is Ψ= Φ63 whose density is seen to exhibit a uniform circular amplitude characteristic of a liquid state, and (b) a mixed state in the neighborhood of ν =1/3, obtained by disorder-induced coupling between the ground state Φ63 and the adjacent excited state with L1 = 57. The density of the broken-symmetry mixed state Ψ= α Φ57 + β Φ63 (with α = 1/
2,
β =1/
2)
, shown in
blue on the right, exhibits a non-uniform crystalline pattern,
portraying formation of a disorder-pinned wigner crystallite. The
results were obtained through exact diagonalization of the hamiltonian,
with the parameters corresponding to GaAs, i.e. a dielectric constant κ =
13.1 and an effective mass m* =0.0067 me, and a confining potential of 3.6 meV. Lengths are given in units of the magnetic length lB, and the units of the vertical
axes are 10−2lB-2. The electron density is normalized to the number
of particles, N.
