Quantum interference effects in antidot lattices in magnetic fields

A numerical study is performed on quantum interference effects in antidot lattices in a weak magnetic field with the use of a recursive Green's function technique. An irregular Aharonov-Bohm (AB)-type oscillation varying sensitively with antidot diameters and periods is dominant in ideal antidot lattices. The AB-type oscillation disappears and an Al'tshuler, Aranov, and Spivak (AAS) oscillation manifests itself in the presence of fluctuations in the size or position of antidots. The AAS oscillation is much stronger in hexagonal lattices than in square lattices, in good agreement with experiments.