Self-consistent Force Constant Calculation for a Two-dimensional Wigner Electron Crystal in High Magnetic Fields, and Limitations of Lindemann's Law of Melting

Abstract

Abstract The Einstein oscillator model of the Wigner electron crystal takes a specified force constant, which is an explicit function of the electronic separation rs . Here a method is devised for its self-consistent calculation. For the gaussian density of the Wigner oscillator, with width λ in terms of rs , experimental data on the melting temperature Tm versus Landau filling factor v is employed to plot the critical overlap parameter, λ c say, versus Tm . This shows that λ c increases as Tm decreases, which is in contrast to Lindemann's Law.