Quantum corrections to the conductance of a square quantum dot with soft confinement

We study the conductance of a square quantum dot, modeling the potential with a self-consistent Thomas-Fermi approximation. The resulting potential is characterized by level statistics indicative of mixed chaotic and regular electron dynamics within the dot in spite of the regular geometry of the gates defining the dot. We calculate numerically, for the case of a quantum dot with soft confinement, the weak localization (WL) correction. We demonstrate that this confining potential may generate either Lorentzian or linear lineshapes depending on the number of modes in the leads. Finally, we present experimental WL data for a lithographically square dot and compare the results with numerical calculations. We analyze the experimental results and numerical simulations in terms of semiclassical and random matrix theory (RMT) predictions and discuss their limitations as far as real experimental structures are concerned. Our results indicate that direct application of the above predictions to distinguish between chaotic and regular dynamics in a particular cavity can not always lead to reliable conclusions as the shape and magnitude of the WL correction can be strongly sensitive to the geometry-specific, non-universal features of the system. Received 13 May 1998