Screening and electronic correlations in quantum wires in strong magnetic fields: Filling factor dependence

The screening of the Coulomb interaction in quantum wires, subjected to strong perpendicular magnetic fields, is assessed for integer filling factors $\nu <~3$ and low temperatures. Correlations due to bulk screening are rather weak whereas those due to screening at the edges are very strong and smoothen considerably the energy dispersion. The group velocity at the Fermi edge $v_g{(k}_{\mathrm{F}\nu })$ can be one order of magnitude larger than the Hartree velocity $v_g^{\mathrm{H}}{(k}_{\mathrm{F}\nu }).\mathrm{}$ The exchange-correlation contribution $v_g^{\mathrm{ec}}{(k}_{\mathrm{F}})$ to $v_g{(k}_{\mathrm{F}})$ is proved to be nonsingular and for sufficiently strong magnetic fields $v_g^{\mathrm{ec}}{(k}_{\mathrm{F}})$ is proportional to $v_g^{\mathrm{H}}{(k}_{\mathrm{F}\nu })$ with a proportionality constant that depends on $\nu .$ The dispersion relation, obtained in the screened Hartree-Fock approximation, is in line with the observed strong suppression of the spin splitting for $\nu =1\mathrm{}$ and helps explain the observed destruction or absence of some quantum Hall states. For $\nu =2\mathrm{}$ the effective $g_{\mathrm{op}}^{*}$ factor is constant whereas for $\nu =1\mathrm{}\left(3\right)\mathrm{}$ varies strongly across the channel. In addition, the calculated activation energies agree well with those determined experimentally.