MOBILITY EDGE IN A FRACTAL SYSTEM

We consider the nature of the eigenstates of a tight-binding model def ined on a particular class of fractal trees which may have a nonintege r spectral dimension greater than 2. By using the transfer matrix meth od, an analytical expression for the localization length is obtained f or the entire range of energies E. Based on the analytical expression, it is shown that the tight-binding model defined on these peculiar fr actal trees can exhibit a mobility edge.