Magnetoresistanceoscillations periodic with respect to the flux h/e have been observed in submicron-diameter Au rings, along with weaker h/2e oscillations. The h/e oscillations persist to very large magnetic fields. The background structure in the magnetoresistance was not symmetric about zero field. The temperature dependence of both the amplitude of the oscillations and the background are consistent with the recent theory by Stone.

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A modified Young's double-slit experiment is realized for electrons in a high-mobility two-dimensional electron gas (2DEG). The observed quantum interference is employed to study dephasing by electronelectron interaction on length scales shorter than the elastic mean free path. It is found that the measured phase-breaking length agrees very well with theoretical calculations of the e-e mean free path in an ideal 2DEG. In contrast to the diffusive regime, dephasing occurs via e-e scattering events with an energy exchange on the order of the carrier excess energy.PACS numbers: 73.40.-c Electronic interference phenomena in solid-state systems and their destruction by electron-electron interaction have been extensively studied both theoretically and experimentally in recent years. Examples include weak localization, Aharonov-Bohm oscillations in small rings, universal conductance fluctuations in mesoscopic conductors, and the magnetoresistance of narrow wires. All these studies, however, were concerned with diffusive electronic motion where the elastic mean free path l e was the shortest relevant length in the system. In particular, in all of these experiments and corresponding theories, the e-e mean free path l e . e , as well as the phase-breaking length / 0 , has been much longer than l e . Here we are concerned with the opposite limit, the ballistic one (as far as phase breaking is concerned), where l e >: /^. Macroscopic transport in this case is expected to be purely classical and the experiment presented below was therefore carried out on length scales smaller than or comparable to both l e and 1$.In Fermi-liquid theory, the dephasing time is a key parameter that determines the quasiparticle lifetime. An experimental determination of this quantity, and its dependence on different parameters in the various regimes, is therefore of great importance in testing our theoretical understanding of an interacting two-dimensional electron gas (2DEG). A more practical motivation originates from the need to predict the constraints on operation of electronic devices based on quantum interference phenomena. For the diffusive case, l^le, it was shown by Altshuler, Aronov, and Khmelnitzkii l that for dimensionality equal to or lower than 2, and low enough temperatures, phase is lost due to e-e scattering events characterized self-consistently by an energy exchange on the order of h/r^ (T^, is the phase-breaking time). For 2D conductors, this energy is smaller than the temperature ksTby a factor kfle/lnikfle)^ 1 (k F is the Fermi wave vector). The quasiparticle energy is therefore a well-defined quantity as required for a quasiparticle description of a Fermi liquid. The resulting phase-breaking time is considerably shorter than the en-ergy relaxation time, which is governed by scattering events with an energy exchange on the order of kgT.The importance of small-energy scattering events for dephasing in ID wires was confirmed experimentally by Wind et at. 2 For the ballistic case, we are not aware of any detailed discussion o...

Electrostatic focusing of ballistic electrons in a high-mobility two-dimensional electron gas is discussed and experimentally demonstrated. The focusing is achieved by a spatial modulation of the electrostatic potential along the electrons trajectories, in analogy with the modulation of the dielectric constant in conventional light-wave optics.The long electronic mean free path (mfp) in twodimensional electron-gas (2D EG) systems and improved electron-beam lithography have opened a new field of research which might be called "electron optics in solids. "A few recent examples are magnetic focusing, ' the collimation of an electron beam injected from a smooth con-