Kosterlitz-Thouless transition in a finite size system

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The Wigner crystal transition is investigated for electrons confined in the quasi one dimensional channels (5, 8, and 15 μm). In the crystal phase, the transport of the electrons is nonlinear because of the Bragg-Cherenkov (BC) of ripplons. We find that the temperature at which the BC scattering disappears increases with decreasing the number of electrons across the channel. This temperature agrees with the temperature at which free dislocations emerge in the channel due to the Kosterlitz-Thouless mechanism.