Magnetotransport and Persistent Currents in Ballistic Microstructures
In this Thesis we discuss properties of different ballistic microstructures in the presence of a magnetic field. Three topics have been studied: (i) the magnetoconductance of a three-dimensional (3D) microwire, (ii) magnetotransport and persistent currents in a two-dimensional so called "quantum dot" in a gated AlGaAs heterostructure, and (iii) some magnetotransport properties of a quasi one-dimensional conducting channel in the same kind of material.
For the 3D ballistic microwire our theory predicts a new type of step-like fluctuations in the magnetoconductance and sharp "spikes" in the thermopower coefficient. These mesoscopic fluctuations, which appear on a new scale corresponding to a small fraction of the quantum unit of magnetic flux Fo = hc/e, are a novel manifestation of the Aharonov-Bohm effect. The sharp conductance steps are caused by the shift of electronic levels through the Fermi level in a magnetic field. We discuss the effect of thermal smearing and scattering effects and conclude that the flux-induced steps should be observable in e.g. submicron Bi whiskers at T ~ 0.1 K. Sample-characteristic fluctuations are predicted to appear in fields as low as a few Gauss.
In the second part of the Thesis we present a theoretical description of persistent currents in a 2D ballistic quantum dot. The equilibrium ground state of this mesoscopic system sustains a persistent current. Depending on the relevant relaxation rate, the system can be driven out of equilibrium by a time dependent magnetic field. Two critical relaxation rates (and temperatures) are found where the characteristic current oscillations are smeared. We also propose a method for measuring relaxation times of the system by monitoring the current relaxing to a new equilibrium value after a sudden change in magnetic field.
In the third part of the Thesis we calculate numerically the self-consistent potential for electrons moving in a narrow, quasi one-dimensional channel formed in a gated AlGaAs heterostructure. The channel width, the shape of the self-consistent potential, and the number of occupied modes is studied as a function of gate voltage. We solve numerically for the adiabatic edge states and the forward scattering rates caused by a curved channel boundary. The critical values of the B-field for transition into mixed-mode transport is calculated. Scattering involving the innermost edge state (highest Landau level index) is found to be very inefficient for certain values of the magnetic field where this mode "decouples" from the lower-index modes. This behavior is consistent with recent experimental observations.