Time dependent impurity in a quantum wire: Applications to spin transport and to probing stable phases of the single impurity wire.

摘要

This thesis is devoted to a study of time-dependent impurity scattering in a one-dimensional system of interacting electrons—a quantum wire. The scattering potential can be characterized by a complex valued parameter, whose periodic variation in time is shown to lead to a time-independent (DC) current in the wire. Using this method of parametric pumping, an experimentally realizable scattering potential is proposed for generating a DC spin current in a wire. The effect of electron-electron interactions on spin and charge current is analyzed; it is shown that repulsive interactions lead to the transport of integer charge 2ne and spin nħ in a single slow pumping cycle.; In Chapters I and II, the notion of parametric pumping is developed by studying the quantum wire with a time-dependent impurity potential. The quantum wire is treated within the Luttinger model which treats interactions between electrons by an effective short-ranged potential. Several calculations are described that derive the dependence of pumped charge and spin on the frequency of pumping. For a special value of interaction strength in the Luttinger model, the time-dependent impurity problem is solved exactly, and shown to give the aforementioned quantized charge transport. Based on these calculations, it is argued that this universal behavior of pumped charge distinguishes a quantum wire from a non-interacting gas of electrons for which the average pumped charge is non-universal.; In Chapters III and IV, a general approach that applies to a class of one-dimensional systems whose elementary excitations have a continuous spectrum (Luttinger liquid) is developed. The pumped spin or charge is related to a generalized non-equilibrium spin or charge conductance. It is shown that, because of interactions in the wire, this quantity is independent of the impurity couplings in the limit of slow pumping. As a consequence, the pumped charge or spin per cycle is a universal number. Specifically, for a particular pumping cycle in a carbon nanotube quantum wire we predict that the pumped charge in the slow pumping limit is 4e, and the pumped spin is 2ħ.