Quantum Adiabatic Electron Transport in Ballistic Conductors

Abstract

The properties of electron transport in small conductors are related to the relevant length scales. In the diffusive transport regime, in which the elastic mean free path l e is much smaller than the dimensions of the conductor (see Figure 13.1a), quantum interference effects can produce deviations from the predictions of classical transport theory. These interference effects result from phase differences acquired by an electron wave in traveling between two points in the sample along different possible trajectories. Many different trajectories can arise from scattering at impurities, resulting in phenomena like one-dimensional (1D) weak localization (for a review, see Chakravarty and Schmid(1)) and universal conductance fluctuations.(2) In a ring, where there are only two sets of possible trajectories from the entrance to the exit, the interference gives rise to periodic conductance oscillations known as the Aharonov-Bohm effect and Al’tshuler-Aronov-Spivak oscillations (for a review, see Washburn and Webb(3)). To observe these quantum interference effects, the distance electrons can travel with conservation of phase coherence, l φ must be larger or at least of the order of the sample dimensions.