Gy. Oh et al., ELECTRONIC-PROPERTIES AND MULTIFRACTALITY OF A ONE-DIMENSIONAL HIERARCHICAL SYSTEM IN THE PRESENCE OF AN ELECTRIC-FIELD, Physical review. B, Condensed matter, 45(12), 1992, pp. 6400-6407
We study the influence of an applied electric field F on the electroni
c properties of a one-dimensional system with hierarchical potential s
trengths. By the method of the Poincare map, we calculate the transmis
sion coefficient T as a function of the system size N. For small field
s, it shows an algebraically localized behavior. With increasing field
strength, a delocalization of the field-induced localized states occu
rs and T shows extended behavior for R < 2 while it retains a power-la
w localized behavior for R > 2. We perform a multifractal analysis on
the wave functions of the field-induced states and find the multifract
al property in the field-induced extended states.