Metal-insulator transition in three-dimensional Anderson superlattice with rough interfaces

Abstract

We study the electronic properties of superlattice with rough interfaces in two and three dimensions using the transfer-matrix method and direct diagonalization of the Anderson Hamiltonian. The system consists of layers with an average constant width, but with stochastic roughness added to the interfaces between the layers. The numerical results indicate that, in the thermodynamic limit, the two-dimensional superlattice is an insulator in the presence of even small roughness. In three-dimensional systems, however, the superlattice exhibits a metal-insulator transition with a well-defined mobility edge located at an energy ${E}_{c}$ that we compute numerically. For three-dimensional superlattice, the localization length follows a power law near the mobility edge $\ensuremath{\xi}(E)\ensuremath{\sim}{({E}_{c}\ensuremath{-}E)}^{\ensuremath{-}\ensuremath{\nu}}$, where the exponent is $\ensuremath{\nu}\ensuremath{\simeq}1.6$. We also show that the existence of the extended states in three-dimensional superlattices gives rise to a finite conductivity in the limit $M/L\ensuremath{\rightarrow}\ensuremath{\infty}$, where $L$ is the length and $M$ the width of the bar.