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We have recently developed a spectroscopic technique which allows direct measurement of quantum energy levels. The method is based on observation of the capacitance signal resulting from single electrons tunneling into discrete quantum levels. The electrons tunnel between a metallic layer and confined states of a microscopic capacitor fabricated in GaAs. Charge transfer occurs only for bias voltages at which a quantum level resonates with the Fermi energy of the metallic layer. This creates a sequence of distinct capacitance peaks whose bias positions directly reflect the electronic spectrum of the confined structure. Using this “single-electron capacitance spectroscopy”, we map the magnetic field dependence of the ground state energies of a single quantum dot containing from 0 to 50 electrons. Along with a spectroscopic measurement of the dot's ground states, we probe tunneling rates of electrons to individual quantum states. The experimental spectra reproduce many features of a noninteracting electron model with an added fixed charging energy. However, in detailed observations deviations are apparent: exchange induces a two-electron singlet-triplet transition, self-consistency of the confinement potential causes the dot to assume a quasi two-dimensional character, and features develop which are suggestive of the fractional quantum Hall effect.

We demonstrate that ballistic electrons in ultra-high mobility two-dimensional electron systems can be controlled in ways analogous to the manipulation of photons in optical systems. Among the electron-optical structures we demonstrate are emitters, detectors, absorbers, and refractors. These advances may enable the design of new types of electronic circuits.

We have observed ballistic electron transport beyond 100 microm in the 2D electron system of an ultra-high mobility GaAs(AlGa)As heterostructure employing a magnetic electron focusing technique through wide point contacts. The amplitude of the characteristic magneto-oscillations is found to depend exponentially on electron propagation distance with a decay length λ a = 15 microm. λ a differs by about a factor of 2 from the mobility mean free path of 28 microm. This may indicate the determination of a different angular average of scattering events in focusing experiments as compared to standard mobility measurements.

The FQHE has been studied in GaAs/AlGaAs heterostructures of mobility 5 × 106 cm2/V·s. Activation energies of the thirds states at v = 13, 23 far exceed earlier results, and comparison is made to theoretical values. These samples allowed observation of quantization in ϱXY at v=27 and v=15. Results from higher density samples display the hierarchical series up to v=613.