DYNAMICS OF ONE-ELECTRON IN A ONE-DIMENSIONAL SYSTEMS WITH AN APERIODIC HOPPING DISTRIBUTION

In this paper, we consider the effect of an aperiodic hopping distribution on a single electron. The aperiodic sequence of hopping energies was generated by using a sinusoidal function whose phase phi varies as a power-law, phi proportional to n(nu), where n labels the positions along the chain. The exponent nu controls the degree of aperiodicity in the sequence hopping terms. Using the transfer matrix method, we compute the localization length within the band of allowed energies. Our numerical calculations indicate that, for an aperiodic sequence of hopping energies with nu < 1, a new phase of extended states appears in this model. For a pseudorandom hopping distribution with nu > 1, all eigenstates remain localized. In addition, we study the electronic dynamics subjected to an electric field. Our numerical calculations reveals perfect Bloch oscillations for nu < 1. The typical frequency of these oscillations agree with the semiclassical predictions.