Cyclotron trapping, mode spectroscopy, and mass enhancement in small GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As rings

A new electronic trapping effect has been observed in a small GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As ring, which takes place when the cyclotron orbits match the loop geometry. The trapping causes peaks in the magnetoresistance R(B) at low fields, and the peak positions were used to study the dispersion relation ${\mathit{E}}_{\mathit{n}}$(k) of the one-dimensional magnetoelectric subbands. This allows the ring to be used as a mesoscopic mass spectrometer. The electron effective mass increases with magnetic field by a factor of 50 at field of 0.5 T. General agreement obtains between the experiment and the subband calculations for one-dimensional channels, indicating that true solid-state interferometers are possible.