The Study Of The Quantized Pumping Effect

The time-dependent electron transport in mesoscopic physics discipline has been inten-sively and extensively studied with the rapid development of nanotechnology.The quantized quantum parameter pump will be decisive to the quantum metrology in that the basic physics quantities such as the electric current unit and frequency need identify.Thouless is the pioneer who first put forward the quantum topologic pump in that a one-dimensional moving potential can pump out an integer number of electrons in a cycle.Since then,to seek a much more convenient and robust quantized pump system is one of the paramount tasks.In this thesis,we will mainly discuss the possible electron and spin quantized pump as well as the intrinsic physics mechanism based on the Dirac electrons in graphene systems and these works will advance the fabrication of new electron pump devices.We systematically study the quantized electron pump effect in the graphene monolayer and multilayer systems as well as the helical states of the topological insulator system.The traditional two-parameter quantum pump model is considered and the nonequilibrium Green's function and scattering matrix method are employed in the study.In the first and second chapter,we present some research context and methodology.The possible quantization of quantum pump induced by the time-dependent lattice distortion is discussed in the third chapter.In the followed chapter,the quantum pump in the graphene monolayer and multilayer systems is studied by considering the time-relying staggered potential from external electric fields.In the chapter V,Both charge and spin pump quantization are studied based on the helical edge states of a topological insulator and the two magnetization precession are introduced as the pumping potentials.In the last chapter,we also present the study of the anomalous spin Josephson effect in a model of static magnetization introduced in a topological insulator system.In the graphene monolayer system,we take the lattice distortion as the pump potentials and show that two integer charges can be pumped out in a pumping cycle when the transport direction is perpendicular to the linear distortion forces.The pumping results are quantized and this is attributed to the fact that there is a topological interfacial state forming in between two pumping potential since these two regions possess different topologic phases.In addition,the quantized pump current phase relation is severely deviating from the usual sine function behavior.In the graphene multilayer system,we consider the possible quantized pump effect by introducing the staggered potentials as the pump parameters which come from the external perpendicular AC electric field.By comparison,we show that the pump quantization can be found in the single-layer and tri-layer graphene systems whereas there is no pump current at all in the bilayer graphene system when the Fermi energy is lying in the effective energy gap due to the staggered potentials.The results are originated from the fact that not only the topological interface state between the two pumping regions is important but the Berry phase of electrons with odd fold of pi is also decisive.In the fifth chapter,we extend the quantized pump model to the helical states of a topological insulator by considering two time-dependent magnetization.It is found that not only the charge quantized pump is possible but also the spin optimal pump is obtainable.Both the pure spin pumped current and spin-fully polarized charge current are shown and depend on many system parameters which can be used to modulate the pump output,including the pumping phase difference,Fermi energy,and the dynamic phase difference of electrons that be controlled via an external gate voltage so as to provide the convenience in experimental measurements.In order to obtained the spin optimal pump,the graphene model by considering a static magnetization which can lead to the magnetization or spin-dependent dynamic phase difference of electrons traveling in between the two pumping regions.In the last chapter,we study the possible anomalous spin Josephson effect based on the topological insulator by considering two static magnetization to realize a spin superconductor.It is shown that there is a spin supercurrent flowing between two magnetization when the magnetization are noncollinear,but the current phase relation is similar the traditional ?0 superconductor junction.The physics is ascribed to the definite chirality of electrons of the helical edge states and the magnetic coupling different from the usual coupling in the conventional materials is further indicated.To conclude,we have investigated the possible quantization of parametric pump in the traditional two-parameter pump model to realize perfect optimal charge and spin pump.The underlying origin is the introduced pumping potential capable of inducing a new topological phase and forming a topological interface state which evolves with time to foster the pump current.Another important factor in formation of the quantized pump is the condition that the electron has a Berry phase with an odd fold of ?.