A classical model for the magnetic field-induced Wigner crystallization in quantum dots

A classical model is presented for magnetic field-induced Wigner crystallization in electron systems confined within two-dimensional quantum dots. In contrast to other classical models, this one does not treat an electron as a point charge; the electron density is assumed to take a Gaussian form corresponding to the lowest Landau level. Using a Monte Carlo method we have determined the equilibrium configurations as functions of the magnetic field. We have found a classical counterpart of the quantum maximum density droplet (MDD) and studied the breakdown of the MDD into a Wigner molecule as well as the transformations of the Wigner molecule shape induced by the external magnetic field. The phase diagram for the classical Wigner molecules has been presented and its qualitative agreement with previous quantum mechanical calculations has been shown.

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