Size-dependent effects on the magnetotransport fluctuations of square quantum dots

Recently, experimental studies of magnetotransport in nominally square quantum dots have revealed a high degree of periodicity in the conductance fluctuations, with only a few apparently harmonically related frequencies dominating the power spectra. Analysis of dots of different sizes has revealed that there are unresolved issues regarding the scaling of the dominant frequency of the fluctuations. The experimental data appear to suggest that the dominant frequency scales with A^1/2, where A is the area of the dot. On the other hand, a semiclassical analysis of periodic orbits suggests that the scaling should be with area. In this paper, we attempt to resolve this issue by simulating dots of many different sizes using both quantum mechanical and classical approaches.