Energy Spectra of Interacting Two-Dimensional Electrons in a Magnetic Field

Abstract

The eigenstates of interacting two dimensional electrons in a magnetic field are studied theoretically for the case when the electron wave functions are subject to periodic boundary conditions. Classifying the states according to the irreducible representations of the appropriate magnetic space group enables them to be computed efficiently and leads to a detailed picture of their degeneracies. Numerical results for small systems are presented to show how the energies of the lowest few states depend on the number of flux quanta present and on the aspect ratio of the system. The energy spectra at various filling factors are found to behave differently when either the number of flux quanta or the aspect ratio are changed. In particular, when the aspect ratio is small the ground state energy has cusplike minima at l/n fractional filling but the minima at even order fractional filling tend to disappear when the aspect ratio is increased. The energies of the low lying excited states also depend on aspect ratio but do not always have minima at l/n filling. These effects are explained in terms of a competition between direct and exchange interactions which favours clustered configurations of electrons when the aspect ratio is large. The finite size scaling of the energy levels is briefly discussed.