Abstract
The melting criterion of the two-dimensional Wigner crystals is studied at zero temperature by taking into account of phonon anharmonicity. The lowest order anharmonic corrections do not lead to the phonon instability, where the shear modulus of the Wigner crystal vanishes, in contrast to the earlier calculation by Chang and Maki, and the next order corrections are shown to be important to have the phonon instability. On the assumption that the phonon instability causes melting, we find that the melting occurs at r s ∼ 8.7. This value is in good agreement with the recent experiment in Si MOSFET's by Pudalov et al.
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