Tunneling between edge states in clean multiple GaAs/AlxGa1-xAs rings and increase of the phase coherence length with magnetic field

Abstract

In GaAs/AlxGa1-xAs coupled four-ring and two-ring samples, large Aharonov-Bohm (AB) oscillations have been observed for magnetic fields 0<B<4.5 T. The oscillation spectrum changes systematically corresponding to the subband (Landau level) population inside the one-dimensional channels. Multiple tunneling between the edge states encircling the lithographically defined islands causes well-resolved high harmonics ne/h of the fundamental Aharonov-Bohm oscillation frequency with n≤8. Such high harmonics indicate participation from several islands and require very long phase coherence lengths lφ. The frequencies fn=ne/h of all harmonics decrease with increasing B in accord with a simple model. These findings are evidence for ballistic transport in these large complex devices. The B dependence of the quantum interference amplitudes Gn(B) for AB oscillations of frequency ne/h is qualitatively different from the previously published results: They increase by about an order of magnitude with increasing B before decaying at very high field. The increase in Gn(B) is exploited to infer lφ and indicates that lφ(B) increases with B at a rate 1.3 μm/T. © 1994 The American Physical Society.