Localization–delocalization transition in two-dimensional system with correlated disorder

We study the localization properties of the two-dimensional (2D) Anderson model with diagonal correlated disorder named visible vw and non-visible nw sites. Using the exact diagonalization of Anderson Hamiltonian, investigating the behavior of the density of states (DOS), we found that states in the center of the band E=0E=0 show critical behavior. The energy levels statistics (ELS) is also examined, we found a crossover of the nearest-neighbor level spacing distribution P(s)P(s) from Wigner Surmise distribution at small correlated disorder vw and nw (indicating a metallic behavior) to the Poisson distribution at large correlated disorder vw and nw characteristic for localized states. In addition, an analysis of width M   dependence of the reduced localization length λ/Mλ/M is obtained by the transfer-matrix method (TMM). For all investigated strengths of correlated disorder at E=0E=0 and E=+2E=+2, the reduced localization length λ/Mλ/M always decreases with increasing width. We found only delocalized states in suggested energy and disorder range.