Effect of disorder on quantum localization in 2D AxB1−x binary crystals

Abstract

A 2D square lattice with nearest neighbor interactions (V0) and periodic boundary conditions is used to analyze the quantum localization of eigenstates of a binary mixed crystal in the split-band limit. The lattice sites are randomly occupied either by A molecules with energy EA = Δ at concentration x or by B molecules with energy EB = −Δ at concentration 1 − x. Because of the random distribution of the molecules the general Hamiltonian implicitly accounts for both diagonal and off-diagonal disorders. The full diagonalization of the Hamiltonian provides all eigenstates in the energy domains of A and B from which the inverse participation ratios (IPR) and their band averages ⟨L⟩E are evaluated and configurationally averaged. The two limiting cases Δ ⩾ V0 and Δ ≅ V0 are investigated and compared. In the latter case it is shown that the statistical fluctuations are smoothed out relative to that of the infinite split-band. Furthermore, our results show a gradual decrease of the band averages when increasing x and a strong dependence on Δ.