Self-similar magnetoconductance fluctuations in quantum dots

Self-similarity of magnetoconductance fluctuations in quantum dots is investigated by means of a tight binding Hamiltonian on a square lattice. Regular and chaotic dots are modeled by either a perfect $L\times L$ square or introducing diagonal disorder on a number of sites proportional to L. The conductance is calculated by means of an efficient implementation of the Kubo formula. 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 controlled by the ratio $W/L.\mathrm{}$ The fractal dimension decreases from 2 to 1 when $W/L$ increases from $1/L$ to 1, and is almost independent of other parameters such as Fermi energy, leads configuration, etc. This result is consistent with recent experimental data for soft-wall cavities, which indicate that D decreases with the degree of wall softening (or, alternatively, cavity opening). The results hold for both regular and chaotic cavities.