Characterization of the electronic states in weakly disordered one-dimensional systems

The problem of characterization of electronic states in disordered systems is readdressed. For this task, we present our ensemble-averaged calculations of both density of states and de-conductivity for linear chains containing up to 3500 sites and modeling the Anderson Hamiltonian with on-site energies randomly chosen from a box distribution of width W. The analysis of the spatial behaviour of eigenfunctions when increasing the disorder shows an increase of the curdling of the wavefunction amplitude, which reflects a stronger localization. The de-conductivity results show that, for low disorder W/V < 2, the states at the midband seem to have localization length λ at least as large as the system sizes considered here. For larger disorder, the system exhibits "almost an Anderson transition" between localized and quasi-extended states, which are localized with very large λ. Our de-conductivity results suggest a critical fractal dimension d_c* = 0.70 ± 0.09 to discriminate between the exponentially and the power-law localized states. The relatively large error bar Δd_c* may reflect the nature of a continuous transition between the two regimes.