Electron-electron scattering in a two-dimensional electron gas in a strong magnetic field

The electron-electron scattering rate 1/τ is calculated for two-dimensional electrons in a strong magnetic field B and a smooth random potential. The temperature T=0 and all the electrons are in the lowest Landau level. The random potential is assumed to depend only on one coordinate. (This model is shown to be invalid only if the energy of the test electron ɛ is in the very tail of the Landau level density of states or close to the Fermi level ɛ_F). Contrary to the case of B=0 when 1/τ~(ɛ-ɛ_F)², for B≠0 the scattering rate is suppressed for electrons far from the Fermi level, 1/τ~(ɛ-ɛ_F)^-1.