Excitonic ions and pseudopotentials in two-dimensional systems: Evidence for quantum Hall states of anX−gas

Abstract

Systems of up to 12 electrons and six holes on the Haldane sphere are studied by exact numerical diagonalization. The low-lying states of the system involve bound excitonic complexes such as ${X}_{n}^{\ensuremath{-}}.$ The angular momenta of these complexes and the pseudopotentials describing their interaction are determined. The similarity to the electron pseudopotential suggests the possibility of incompressible ground states of a gas of ${X}^{\ensuremath{-}}$ ions for $\ensuremath{\nu}<~1/3.$ The $\ensuremath{\nu}=1/3$ states of three and four ${X}^{\ensuremath{-}}$'s are found.