The temperature dependence of the amplitude of the Aharonov-Bohm ͑AB͒ oscillations in a single mode ballistic ring has been measured. The experimental data is analyzed using the exact energy spectrum of an ideal ring with a finite width and the Landauer-Büttiker formula to calculate the conductance of the ring. We show that the temperature dependence of the AB oscillations can be explained in terms of the thermally averaged transmission probability through the energy levels of the ring provided the additional charging energy is taken into account. This demonstrates the effect of Coulomb repulsion on the AB oscillations in a ring interferometer.

Shubnikov-de Haas oscillations are measured in wide parabolic quantum wells with five to eight subbands in a tilted magnetic field. We find two types of oscillations. The oscillations at low magnetic fields are shifted toward higher field with the tilt angle increasing and can be attributed to two-dimensional Landau states. The position of the oscillations of the second type does not change with increasing the tilt angle which points to a three-dimensional character of these Landau states. We calculate the level broadening due to the elastic scattering rate ⌫ϭប/2, where is the quantum time, and the energy separation between two-dimensional subbands, ⌬ i j ϭE j ϪE i , in a parabolic well. For all levels we obtain ⌫ j ϳ⌬ i j , which means that the levels overlap, supporting the observation of three-dimensional Landau states. Surprisingly, we find that the lowest subband, which has a smaller energy separation from the higher level, does not overlap with these subbands and forms a two-dimensional state.