Abstract

The single-parameter scaling theory of localization
describes the behavior of disordered systems in integer dimensions and
predicts the existence of repulsive metal-insulator critical point in
two dimensions in presence of weak antilocalization. I will show that fractals
allow to continuously tune the dimensionality Anderson
localization transition. This allows to create a new, attractive critical
point of the scaling flow of conductance by continuously tuning the
fractal dimensions. Unlike the regular metal-insulator transition, this
attractive fixed point may only appear in fractal dimensions.