Anomalies and Anderson localization: π-coupling of the energy bands

This work shows that delocalization phenomena in single-electron quasi-one-dimensional quantum chains may occur at points different from the center of the energy spectrum (E = 0) and in systems lacking the symmetry E -> - E. It is found that the peaks appearing in the average conductance are controlled by the band structure of the periodic system underlying the disorder. The average conductance is expanded in powers of the disorder strength, allowing the conductance to be redefined as the sum of a regular and an anomalous contribution. The first non-vanishing term of the anomalous part is of the fourth order. The fourth-order term can be calculated for any number of coupled chains in terms of a matrix expression. For strictly one-dimensional systems the expansion is calculated up to the 12th order for both diagonal and real off-diagonal disorder and is compared with the numerical data. It is also found that the anomalous contribution defined here is responsible for an even-odd effect of the average conductance.