Finite-size studies of the FQHE-electron solid phase transition using a non-orthogonal localised basis set

Abstract

Finite-size calculations are used to study the variation of the ground state of the interacting two-dimensional electron system with varying magnetic field. Of specific interest is the phase transition from the fractional quantum Hall liquid state to the crystalline solid ground state. A novel localised basis set is used for the calculations, which is expected to generate a better approximation to the crystalline state than previous bases. Hexagonal symmetry into the pair-correlation function, together with an increased peak to valley ratio showing an enhanced level of localisation of the electrons, is taken as an indication of the presence of the crystalline state. First indications of hexagonal symmetry are at filling factors just greater than 1 5 , which is in good agreement with experiment. The hexagonal symmetry becomes distinct for filling factors between 1 5 and 1 7 , but is absent at exactly 1 5 filling. This is taken to indicate a re-entrant liquid phase at 1 5 filling as observed experimentally. There is no evidence of a re-entrant liquid phase at 1 7 filling.