Quantum interference effects and spin-orbit interaction in quasi-one-dimensional wires and rings

We study two kinds of quantum interference effects in transport–the Aharonov-Bohm effect and the weak-localization effect–in quasi-one-dimensional wires and rings to address issues concerning the phase-coherence length, spin-orbit scattering, and the flux cancellation mechanism which is predicted to be present when the elastic mean free path exceeds the sample width. Our devices are fabricated on GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As and pseudomorphic ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$As heterostructure materials and the experiments carried out at 0.4–20 K temperatures. In the GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As devices which exhibit no significant spin-orbit scattering, we were able to extract a phase-coherence length ${\mathit{l}}_{\mathrm{\phi }}$ from the amplitude of the Aharonov-Bohm magnetoresistance oscillations in different sized rings. We find it to be in agreement with ${\mathit{l}}_{\mathrm{\phi }}$ deduced from the weak-localization data in parallel wires when the one-dimensional weak-localization theory including the flux cancellation mechanism is used to fit the data. We therefore unambiguously establish that the same ${\mathit{l}}_{\mathrm{\phi }}$ governs the behavior of the two quantum interference phenomena of Aharonov-Bohm oscillations and weak localization, and that the flux cancellation is in force. In the pseudomorphic ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$As heterostructure devices which exhibit strong spin-orbit interaction effects, ${\mathit{l}}_{\mathrm{\phi }}$ exceeds the spin-orbit-scattering length at low temperatures. The amplitude of Aharonov-Bohm oscillations can only be explained by introducing reduction factors due to spin-orbit scattering.