Electronic correlations in quantum wires subjected to strong magnetic fields: Dependence on the filling factor

Electron-electron interactions and their effects on Landau levels in quantum wires (QWs), subjected to strong perpendicular and parallel magnetic fields, are discussed. For QWs in strong perpendicular magnetic fields, with integral filling factor (&ngr; = 1, 2, and 3), the screened Coulomb interactions are assessed by solving the integral equations for the screened potential, both analytically and numerically. Correlation energy strongly smoothens the energy dispersion in the vicinity of the Fermi level. The exchange-correlation contribution $vecgkF$ to the Fermi-edge group velocity v_g( k_F) is proved to be nonsingular. The energy dispersion, obtained in the local density approximation (LDA), is in line with the observed strong suppression of the spin splitting (&ngr; = 1, 3) and helps in explaining the observed destruction or absence of some quantum Hall states. For QWs in strong parallel magnetic fields, with only the lowest LL occupied, the many-body corrections have a stronger effect on the spin-splitting than in the case of perpendicular magnetic fields.