Electronic properties and multifractality of a one-dimensional hierarchical system in the presence of an electric field

We study the influence of an applied electric field F on the electronic properties of a one-dimensional system with hierarchical potential strengths. By the method of the Poincaré map, we calculate the transmission coefficient T as a function of the system size N. For small fields, it shows an algebraically localized behavior. With increasing field strength, a delocalization of the field-induced localized states occurs and T shows extended behavior for R<2 while it retains a power-law localized behavior for R>2. We perform a multifractal analysis on the wave functions of the field-induced states and find the multifractal property in the field-induced extended states.