Turkish Journal of Physics

Formation of the Triangular Cluster in the Fractional Quantum Hall Regime






The electron-electron (e-e) interactions in MOSFET- and GaAs-AlGaAs quantum wall structures are shown to give rise to appearance of a weak attraction between three electrons. One electron in the e-e interaction process can be trapped in inversion layer into the holes of uncompansated ionized acceptor in the depletion layer. This process is a time reversal one. By applying an unitary transformation the effective Hamiltonian is obtained, which charactarize the formation of triangular electron cluster. It is shown that three-electron effective potential will be attractive. The formation of a triangular electron cluster in two dimensional electron gas seems to be sufficient to understand the Fractional Quantum Hall effect, [1]. In a strong magnetic field the clusters will rotate around the axis, which crosses through the center of a cluster. The minimum value of the cluster's angular momentum is m=3, since the electron cluster become invariant under \pi /over 3 rotation. The Laughlin's wave function [2] for three electron cluster with m=3 should give the charge fraction, e^{\ast} =e /over 3. The result obtained are valid for small value of temperature and impurity concentration. The triangular clusters are unbound with increasing temperature.

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