Properties of a Unique Type of Critical State in the Two-Dimensional Two-Band Anderson Lattice Model in the Presence of Site-Selective Disorder

Abstract

The two-band Anderson lattice model is a minimum model for compounds where the bands near the Fermi energy arise from the hybridization among different atoms. In the presence of site-selective disorder via atomic doping, we show by using the standard transfer matrix method that a unique type of critical state appears at the edge of a less disorder-affected band but with strong van Hove singularity, the asymptotic localization length λ M neither depends on the lateral size M nor the disorder strength W . λ M is five orders of magnitude larger than the lateral size and increases linearly with sample size up to the largest layer number L =10 9 the machine can handle. λ M / L approaches a constant signifying the existence of a critical state at this particular energy. Except for the localization length for this energy, the reduced localization lengths for all other energies in both bands satisfy the single-parameter scaling law and the scaling parameter ξ is obtained and compared. The two-band lattice model with site-selective disorder has the advantage of simulating both diagonal and off-diagonal disorders over the one-band model, and the disparity between electron- and hole-doped bands can be attributed to such nonuniform disorder.