Self-similar magnetoconductance fluctuations in quantum dots

Self-similarity of magnetoconductance fluctuations in quantum dots is inves tigated by means of a tight binding Hamiltonian on a square lattice. Regula r and chaotic dots are modeled by either a perfect L X L square or introduc ing diagonal disorder on a number of sites proportional to L. The conductan ce is calculated by means of an efficient implementation of the Kubo formul a. The degree of opening of the cavity is varied by changing the width W of the connected leads. It is shown that the fractal dimension D is controlle d by the ratio W/L. The fractal dimension decreases from 2 to 1 when W/L in creases from 1/L to 1, and is almost independent of other parameters such a s Fermi energy, leads configuration, etc. This result is consistent with re cent experimental data for soft-wall cavities, which indicate that D decrea ses with the degree of wall softening (or, alternatively, cavity opening). The results hold for both regular and chaotic cavities.