On the Coulomb–dipole transition in mesoscopic classical and quantum electron–hole bilayers

We study the Coulomb-to-dipole transition which occurs when the separation d of an electron–hole bilayer system is varied with respect to the characteristic in-layer distances. An analysis of the classical ground state configurations for harmonically confined clusters with N ⩽ 30 electron–hole pairs reveals that the energetically most favourable state can differ from that of two-dimensional pure dipole or Coulomb systems. Performing a normal mode analysis for the N = 19 cluster it is found that the lowest mode frequencies exhibit drastic changes when d is varied. Furthermore, we present quantum-mechanical ground states for N = 6, 10 and 12 spin-polarized electrons and holes. We compute the single-particle energies and orbitals in self-consistent Hartree–Fock approximation over a broad range of layer separations and coupling strengths between the limits of the ideal Fermi gas and the Wigner crystal.