One-Dimensional Extended States in Partially Disordered Planar Systems

We obtain analytically a continuum of one-dimensional ballistic extended states in a two-dimensional disordered system, which consists of compactly coupled random and pure square lattices. The extended states give a marginal metallic phase with finite conductivity $\sigma_{0}=2e^2/h$ in a wide energy range, whose boundaries define the mobility edges of a first-order metal-insulator transition. We show current-voltage duality, $H_{\parallel}/T$ scaling of the conductivity in parallel magnetic field $H_{\parallel}$ and non-Fermi liquid properties when long-range electron-electron interactions are included.