Ballistic weak localization in regular and chaotic quantum-electron billiards

We report systematic numerical studies of the weak localization (WL) effect in ballistic quantum dots with nominally square geometry similar to that studied in the recent experiments of Bird et al. [Phys. Rev. B 52, 14336 (1995)]. Conductance through the dot is calculated within the Landauer formalism, where dot openings are modeled as quantum point contacts connected to reservoirs. We find that at sufficiently low temperature ballistic fluctuations due to coherent mode mixing inside the dot obscure any average features in magnetoresistance. As the temperature increases, conductance oscillations are smeared out and dot resistance is well described within the Ohmic addition of resistances of two independent quantum point contacts. We demonstrate, as the Ohmic behavior is established, that the shape of the WL peak of a square dot follows the unusual linear dependence predicted by semiclassical theory for geometries for which the corresponding classical dynamics is regular. With a greater number of propagating states in the leads, the agreement with the semiclassical linear behavior is improved. The physical reason for this is given. Effect of the rounding of dot corners and leads (which simulates the change of the potential with decreasing gate voltage in a real device) on magnetoconductance through the dot is investigated. We find that the magnetoconductance is quite robust to rounding of the leads, whereas a relatively small rounding of corners inside the dot is sufficient to destroy regular motion of electrons. This may explain a transition from the linear to the Lorentzian dependence of the WL peak (the latter, according to the semiclassical theory, is characteristic for chaotic billiards) which was detected in the experiment. We also discuss effects of the real potential inside the dot on the shape of the WL peak. © 1996 The American Physical Society.