The microscopic picture of the integer quantum Hall regime

Computer modelling of the integer quantum Hall effect based on self-consistent Hartee-Fock calculations has now reached an astonishing level of maturity. Spatially-resolved studies of the electron density at near macroscopic system sizes of up to $\sim 1\ \mu m^2$ reveal self-organized clusters of locally fully filled and locally fully depleted Landau levels depending on which spin polarization is favoured. The behaviour results, for strong disorders, in an exchange-interaction induced $g$-factor enhancement and, ultimately, gives rise to narrow transport channels, including the celebrated narrow edge channels. For weak disorder, we find that bubble and stripes phases emerge with characteristics that predict experimental results very well. Hence the HF approach has become a convenient numerical basis to \emph{quantitatively} study the quantum Hall effects, superseding previous more qualitative approaches.