Scale factor mapping of self-similarity in semiconductor billiards

Employing three geometries, the relationship between exact and statistical self-similarity (ESS/SSS) in the magneto-conductance of semiconductor billiards is investigated using correlation analysis. A comparison of the three geometries indicate that the form of self-similarity is determined by the design of the Sinai diffuser. The empty square, where the Sinai diffuser is absent, generates SSS. Incorporating a Sinai diffuser into the sidewall of a square also generates SSS. However, insertion of an antidot Sinai diffuser induces the transition to ESS. Inserted at the billiards center, the antidot Sinai diffuser significantly disrupts the electron trajectories.