Correlations between Aharonov-Bohm effects and one-dimensional subband populations in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As rings

The Aharonov-Bohm (AB) interference patterns in ring-shaped conductors are usually dominated by random features. The amplitude of the oscillations is random from sample to sample and from point to point on the magnetic field axis owing to random scattering of the electron trajectories by impurities within the wires. We report experiments on devices made with wet etching and global gates, which have shown major progress towards removing the random features. In loops that exhibit ballistic conductance plateaus and cylotron orbit trapping at 4.2 K, the random pattern of AB oscillations (observed for T<0.1 K) can be replaced by a much more ordered one—especially if only a few transverse modes are populated in the ring. The amplitude and shape of the oscillation envelope function change systematically as subbands are populated in the wires forming the loops. Mechanisms governing the AB effect in the ballistic regime are discussed. Correlation has been found between the G(${\mathit{V}}_{\mathit{g}}$,B=0) staircase and the beating period of the envelope functions. Quantum oscillations in G(${\mathit{V}}_{\mathit{g}}$,B=0) are consistent with direct interference of paths of unequal length. Both the correlations and the quantum oscillations in gate voltage are signatures of ballistic transport.