Tunneling between edge states in clean multiple GaAs/AlxGa1

J. Liu

¹

,

Wei Gao

²

,

K. Ismail

³

et al.

Abstract

In GaAs/Al Gaq As 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 Ls The fre. quencies f"= 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 G"(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 G"(B) is exploited to infer Ls and indicates that Ls(B) increases with B at a rate ) 1.3 Lsm/T.

Quantum Mechanics in Quantum Rings

“…Shubnikov-de Haas oscillations set in at about 2 T where R c ≈ ∆ r. The inset shows that AB oscillations with a slightly reduced period between 65 and 70 mT persist even in the regime where r 0 < R c < ∆ r, but they are hardly discernible at higher fields. The reduced period reflects the increased area enclosed by the A reduction of the AB oscillation amplitude in high magnetic fields has also been observed in earlier experiments on ring structures [9,14,15]. In the remainder of this review we concentrate on measurements in the Aharonov-Bohm regime at B < 0.9 T where the effects of the magnetic field on the orbital wave functions play a minor role but B acts mainly on the wave function phase.…”

Quantum rings for beginners: energy spectra and persistent currents

“…Early experiments in the eighties and nineties reported observations of Aharonov-Bohm oscillations and persistent currents in metallic (Au or Cu) rings [15,16,17] and in loops in GaAs heterojunctions, i.e. two-dimensional electron gas [18,19,20,21,22,23,24]. A related effect which has received recent theoretical [25,26,27,28,29] and experimental [30,31,32,33] attention, is the occurrence of a spin Berry phase [34] in conducting mesoscopic rings.…”

“…Also observations of other periodicities, or higher harmonics, have been reported [24,40] but they have been interpreted as effects of the nonperfectness of the rings. Very recently, the first observation of the inherent Φ 0 /N periodicity, which should appear in perfect very narrow rings, was reported [41].…”

Transmission properties of electron in quantum rings

“…Mailly et al 2 investigated the measurements of the magnetic response of a mesoscopic ring consisting of GaAlAs/GaAs. Large Aharonov-Bohm ͑AB͒ oscillations were observed for magnetic fields 0 Ͻ B Ͻ 4.5 T in GaAs/AlGaAs coupled four-ring and two-ring models by Liu et al 3 Optical emission from a charge-tunable QR and energy spectra of QRs were reported by Warburton and Fuhrer, 4 respectively. Using the Stranski-Krastanov growth mode, high-quality self-assembled semiconductor QRs can be fabricated by solid-source molecularbeam epitaxy 5 to investigate QR properties such as electronic structure and bias-dependent optical transitions.…”