Metal-insulator transitions in anisotropic two-dimensional systems

Abstract

Several phenomena related to the critical behavior of noninteracting electrons in a disordered two-dimensional tight-binding system with a magnetic field are studied. Localization lengths, critical exponents, and density of states are computed using transfer-matrix techniques. Scaling functions of isotropic systems are recovered once the dimension of the system in each direction is chosen proportional to the localization length. It is also found that the critical point is independent of the propagation direction, and that the critical exponents for the localization length for both propagating directions are equal to that of the isotropic system, $\ensuremath{\nu}\ensuremath{\approx}\frac{7}{3}.$ We also calculate the critical value ${\ensuremath{\Lambda}}_{c}$ of the scaling function for both the isotropic and the anisotropic system. It is found that ${\ensuremath{\Lambda}}_{c}^{\mathrm{iso}}=\sqrt{{\ensuremath{\Lambda}}_{c}^{x}{\ensuremath{\Lambda}}_{c}^{y}}.$ Detailed numerical studies of the density of states $n(E)$ for the isotropic system reveal that for an appreciable amount of disorder, the critical energy is off the band center.