Defect states and phase transition in the two-dimensional Wigner crystal

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Abstract
A detailed calculation of the energy of a pair of dislocations in the two-dimensional Wigner crystal is presented. The calculation is based on the "harmonic" approximation of defect theory and shows that the Wigner crystal is unstable against defect generation in that approximation. An analysis of the instability shows that the triangular lattice structure is subject to a rotational instability. It is argued that this instability is the physical cause of the macroscopic polydomain structure observed by Hockney and Brown and the irreversibility of the grain boundary and defect structures observed by Morph at high temperatures.