Quantum transport in nanostructures: From the effects of decoherence on localization to magnetotransport in two-dimensional electron systems

In this thesis, quantum transport in nanostructures is studied theoretically by means of the nonequilibrium Green's function (NEGF) method. Starting with coherent systems, we discuss ballistic transport and conductance quantization in homogeneous tight-binding lattices. We show that disorder gives rise to transmission resonances. A short introduction to Anderson localization is given and a compact analytical formula for the disorder averaged resistance is derived by means of generating functions. Transport in nanostructures generally takes place in an intermediate regime between quantum and classical transport due to decoherence. We study the effects of decoherence on electron transport by a statistical model. The essential idea of our model is to distribute spatially over the system decoherence regions, where phase and momentum of the electrons are randomized completely. The transport in between these regions is assumed as phase coherent. Afterwards, the transport quantity of interest is ensemble averaged over spatial decoherence configurations, which are generated according to a given distribution function. We discuss how homogeneous tight-binding lattices are driven by decoherence from the quantum-ballistic to the classical-Ohmic regime. We show that the transport through disordered tight-binding lattices is affected significantly by the spatial distribution of the decoherence regions. If the decoherence is homogeneously distributed, Ohmic conduction is found for any finite degree of decoherence. In contrast, for randomly distributed decoherence, we find an insulator-metal transition from the localized to the Ohmic regime at a critical degree of decoherence, which corresponds to a critical phase coherence length. We also discuss how transport in disordered tight-binding lattices can be enhanced by decoherence. The decoherence model is extended to obtain pure dephasing. We show that transmission resonances are suppressed by pure dephasing, but the average transmission is conserved. The insulator-metal transition is independent of whether phase randomization goes along with momentum randomization or not. Magnetotransport in two-dimensional electron systems is considered. We study how electrons, coherently injected at one point on the boundary of a two-dimensional electron gas (2DEG), are focused by a perpendicular magnetic field onto another point of that boundary. At weak magnetic field, the generalized 4-point Hall resistance shows equidistant peaks, which can be explained by classical cyclotron motion. When the magnetic field is increased, we observe anomalous resistance oscillations superimposed upon the quantum Hall plateaus. We show that all resistance oscillations can be explained by the interference of the occupied edge channels. The anomalous oscillations are beatings, which appear when only some few edge channels are occupied. By introducing decoherence and partially diffusive boundary scattering, we show that this effect is quite robust. The resistance oscillations can be observed not only in a nonrelativistic 2DEG, but also in the relativistic 2DEG found in graphene. We also report a finite current at armchair edges of graphene ribbons, which is not present at zigzag edges. This edge current can be traced back to the fact that at armchair edges carbon atoms of both graphene sublattices are present, whereas at zigzag edges only atoms of one sublattice appear. The thesis is concluded with some notes on Hofstadter's butterfly shown on the cover page.