Study Of The Electron Transport In Nanometer Structures

The quantum behavior of the electron in the nanometer structures attracts moreand more interests on the design of the novel devices, and leads to many advancesin theoretical understanding of the mesoscopic systems and nanometer structures.In this thesis, the author theoretically study the ballistic transport behavior of theelectron in two dimensional electron gas system based on the multi-mode scatteringmatrix method.In chapter 2, the author firstly study the quantum interference behavior of theelectron through the Young's double-slit interference system in two dimensional elec-tron gas. It is found that, when only the lowest mode is open for conduction inthe three individual slits, the interference patterns of electron flow from the dou-ble slit resemble the results of a conventional Young' s double-slit experiment well.When only the lowest mode is open for conduction in the individual slits, the in-terference patterns of electron flow from the double slit resemble well the results ofa conventional Young' s double-slit experiment. When several modes are open forconduction in the individual slits, the interference patterns of electron flow from thedouble slit are dominated by the interference of electrons flowing through the highestopen modes in the slits and, in general, show rather complex structures. The frontslit plays an important role for a clear observation of interference patterns, whichprovides the coherent source of the electron through the double-slit.In chapter 3, a formulation of the multi-mode scattering matrix method for spin-dependent electron transport in a quantum waveguide with spin-orbit interaction ispresented. All the required Hamiltonian matrices needed in the implementation ofthe formulation are represented in a basis of the transverse spatial eigenstates andthe spin eigenstates of the leads. Thus the method has great flexibility and can beeasily applied to systems with complex geometrical structure, potential distribution,and spin orbit coupling (SOC) strength profile. Also, the method is numericallystable and can be used to treat spin-dependent multisubband scattering processesaccurately. The method has been applied to the spin-dependent electron transportin quasi-one-dimensional conductors, with a region of the Rashba SOC of uniform strength and with a region containing a Rashba SOC superlattice. It is found thatSOC entangles the two spin states and thus leads to the spin polarization. For theconductor with a single region of the Rashba SOC, at strong SOC strengths, thespin-dependent conductance as well as spin polarization show strong Fermi-energydependences. It is shown that the influence of SOI-induced subband coupling on thespindependent transport is particularly strong at Fermi energies close to the onsetsof subbands with the subband index n≥2. However, at a Fermi energy, wherethe total conductance is at a conductance plateau, the spin-dependent conductancesstill show rather regular oscillations with increasing SOC strength or SOC regionlength L. Our results indicate that to achieve a well-controlled spin transistor device,it may not be absolutely required that the SOIincorporated waveguide conductorbe operated in the singlemode conduction regime. For the conductor modulated bya periodic array of strong Rashba SOC regions, the total conductance shows thestandard superlattice behavior. However, the spin-dependent conductances and thespin polarization show complex behavior with regions of slow oscillations and regionsof rapid oscillations. The slow oscillations are found in the energy regions where thetotal conductance is at a plateau. The rapid oscillations appear at energies closeto the onsets of subbands with the subband index n≥2. Because of the complexnature of the spin-dependent conductances, a Rashba SOC-modulated superlatticemay hardly be used as a well-controlled spin-modulating device, although it couldbe used for standard superlattice applications.In chapter 4, the author further study the spin-dependent transport under themodulation of SOC and local magnetic field with the multi-mode scattering matrixmethod. Firstly, the influence of the existence of local magnetic field on the cou-pling of the different subbands is studied. In the absence of the magnetic field, theconductance of electrons shows a series of Fano-resonance type dips in the vicinityof the onsets of subbands with the subband index n≥2. When the local magneticfield is present, the degeneracy of SOC-induced bound states is removed, leading tosplittings of these conductance dips. At two split conductance dips originated fromthe same degenerate dip, a remarkable difference is found in the spatial distributionof spin-projected probability and in the spatial distribution of local spin polarization.It is seen that for a Rashba wire a Hall-like spin accumulation appears at the conduc-tance dips at zero magnetic field. However, in the presence of a local magnetic field a separation of opposite spins along the transport direction is observed in the Rashbawire. In contrast, the zitterbewegung oscillations can show up, when the conductanceis at a plateau, and disappear, when the conductance is at a Fano-resonance typedip, regardless the presence of the local magnetic field.As a further application, in chapter 5, we propose a model which is used torealize the spin filtering upon switching the angular orientation of magnetization inferromagnetic strip. Due to the Zeeman effect, Zeeman splitting gap regions ap-pear close to onset of the subbabds. The in-plane component of local magneticfield is also under consideration in our study which plays an important role for thegeneration of Zeeman splitting gap regions. The theoretical study showed that thespin-polarization can be tuned by switching the angular orientation of magnetizationin the ferromagnetic strip and the spin-polarized transport is strongly dependenton the angular orientation of magnetization when the Fermi energy lies on the halfunit conductance. Such a behavior of the electron transport at the Zeeman split-ting gap regions exhibiting in our system provides a possibility to realize the designof angular orientation of magnetization-control spin filtering device.