Origin of conductance fluctuations in large circular quantum dots

The conductance of large circular quantum dots in high-mobility semiconductor materials displays oscillations as a function of both magnetic field and size. A simple tunneling model has been introduced recently for the interpretation of a particular set of measurements [Persson et al., Phys. Rev. B 52, 8921 (1995)]. In this model it is assumed that the main effect of leads is to make the individual energy levels of the dot Lorentzian broadened while the overall level structure remains essentially the same as for the dot in perfect isolation. This is to be expected for a noninteracting system in the tunneling regime. It has been argued, however, that the model may also be used when leads become open. To examine the validity of this assumption we introduce a supplementary model that consists in a hard-wall circular dot coupled to two conic contacts. At zero temperature such a model predicts a rich structure in the conductance as the Fermi energy is varied. This structure shows little resemblance to the level structure of the isolated dot because the individual states will mix as leads become open. However, the mixing takes place over an energy range that is smaller than energy differences associated with a global shell-like structure that characterizes the spectrum of the dot. As the temperature is raised small scale oscillations are smeared out. Large-scale fluctuations are now compared with the predictions of the simplified tunneling model. An overall qualitative agreement between the two models is found, in particular when leads are placed opposite each other. We therefore conclude that the simple tunneling model is justified under these circumstances and that large-scale fluctuations can be traced to the shell structure and density of states of an isolated circular dot. Support for the tunneling model is also found from visualization of the charge distributions that reveal surprisingly simple and regular patterns. Finally, our model is also briefly discussed in light of the semiclassical periodic orbit theory. © 1996 The American Physical Society.