The advent of semiconductor structures whose characteristic dimensions are smaller than the mean free path of carriers has led to the development of novel devices, and advances in theoretical understanding of mesoscopic systems or nanostructures. This book has been thoroughly revised and provides a much-needed update on the very latest experimental research into mesoscopic devices and develops a detailed theoretical framework for understanding their behaviour. Beginning with the key observable phenomena in nanostructures, the authors describe quantum confined systems, transmission in nanostructures, quantum dots, and single electron phenomena. Separate chapters are devoted to interference in diffusive transport, temperature decay of fluctuations, and non-equilibrium transport and nanodevices. Throughout the book, the authors interweave experimental results with the appropriate theoretical formalism. The book will be of great interest to graduate students taking courses in mesoscopic physics or nanoelectronics, and researchers working on semiconductor nanostructures.

We present studies of the quantum-mechanical transport and the classical billiard transport through ballistic semiconductor quantum dots, where the transport is nonergodic or ''regular.'' These are shown to have quite similar behavior if the classical motion is limited to a collimated set of trajectories. These results are shown to agree substantially with experiments performed on actual semiconductor quantum dots. The results suggest that transport in regular semiconductor quantum dots is clearly distinguished from the equivalent transport in ergodic dots. In particular, the fluctuation spectrum is not random, but highly oscillatory and correlated. The correlation functions for these fluctuations show regular and periodic oscillations that contain only a few, often harmonically related, frequencies. This is fully in keeping with the expectations of semiclassical descriptions of the fluctuations in the density of states of such structures. ͓S0163-1829͑96͒03348-6͔

We determine the phase-breaking time v. @ of electrons in ballistic quantum dots, from the aperiodic fluctuations observed in their low-temperature magnetoconductance. Our analysis shows that at temperatures close to a degree Kelvin v. @ scales roughly inversely with temperature, reminiscent of electron-electron scattering in two-dimensional disordered systems. At much lower temperatures, however, a saturation in r& is observed, with the transition between the two regimes occurring once the thermal smearing becomes smaller than the expected level spacing in the dot. We therefore suggest that the saturation results from a transition from twoto zero-dimensional transport, as the discrete level structure of the dot becomes resolved.Electron interference is an important process in determining the electrical properties of mesoscopic conductors, in which phase coherence of the electron wave function is maintained over considerable distances. ' A thorough understanding of the processes that limit phase coherence is therefore crucial to a complete description of transport in these devices. Such an understanding has already been largely achieved in disordered systems, in which electronic motion is diffusive, and in which phase breaking predominantly results from multiple electron-electron scattering at low temperatures.In contrast, the corresponding processes are less well understood in ballistic systems, although experiment has shown that phase breaking can occur via a single scattering event.No well-established theory for phase breaking exists in this regime, which is perhaps somewhat surprising, given the strong current interest in the electrical properties of low-dimensional structures. In particular, a detailed knowledge of the relevant phase-breaking processes is expected to be of importance in assessing the potential of ballistic electron devices for application in future generations of integrated circuitry.An important time scale for characterizing interference is the phase-breaking time 7. &, the time scale over which the phase of electrons is typically conserved. In this paper we therefore discuss an experimental approach for determining & in ballistic quantum dots. In particular, motivated by the studied of Marcus and co-workers, we obtain an estimate for & from the characteristics of the reproducible Auctuations observed in the low-temperature magnetoconductance. ' As is now well understood, the fluctuations result from interference between electrons ballistically confined within the dot, and their properties have recently attracted much interest as a potential probe for studying the effects of quantum chaos. In a previous study, estimates for 7. & were obtained from the Fourier spectra of the low-field fluctuations observed in a stadium-shaped dot. While the authors were able to obtain values for~& in agreement with recent studies in highmobility quantum wires, ' the approach they employ is only expected to be valid under certain restrictive conditions. In particular, the motion of classical particles in the...

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