QHE, magnetoresistance and disordered transport on 2D mesoscopic plaquettes

The transport properties of a rectangular mesoscopic plaquette in the presence of a perpendicular magnetic field are studied in a tight-binding model with randomly distributed traps. The longitudinal and Hall resistances are calculted in the four-probe Landauer-B\"{u}ttiker formalism which accounts automatically both for the quantum coherence and the trapping-induced localization. The localized character of eigenvectors and the specific aspect of the density of states at a given magnetic flux are correlated with the behaviour of the mentioned resistances as function of the Fermi energy. The Hall insulator and quantum Hall regimes are evidentiated. The dependence on magnetic field of the configurational averages of the longitudinal and Halll resistance is studied in a purely quantum-mechanical approach. Both negative and positive magnetoresistances are found.