Alternating Current Transport Properties For Luttinger Quantum Wires

Correlation(Interaction)and disorder are two basic problem in the condensed matter physics,and they become more important in the low-dimensional system. The electronic transport properties of mesoscopic systems(such as semiconductor heterojunction quantum wire/dot)have been paid much attention.These properties are not only important basic phenomena of physics but also have potential technological applications in the future.The quantum wire and quantum dot etc., will be very important parts of the nanocircuit and quantum information processing. In this thesis,using the Keldysh formalism and equation of motion within the framework of Luttinger-liquid(LL)model,we study the transport properties of interacting quantum wire in the presence of ac fields.And some interesting new results have been predicated for the system,which will help to comprehend problems in interacting low-dimensional system.The thesis consists of seven chapters and is organized as follow:In chapter one we briefly introduce the development history and present research of the Luttinger liquid model,some physical systems that are believed to be described by Luttinger model,and their physical meanings.Chapter two introduces the Bosonization method in detail,and the bosonic expression of the Hamiltonian and other operators are obtained.The contents of from chapter three to six are mainly our work.Chapter three includes two parts.In the first part,using the equation of motion,we investigate theoretically the dynamical ac conductance of a clean Luttinger-liquid quantum wire adiabatically coupled to Fermi liquid electron reservoirs in the presence of short-ranged electron-electron interactions.For a perfect single mode quantum wire,in the limit of zero-ranged interaction we conclude that the static dc conductance ofω→0 is e~2/h,which is independent of the electron interactions.While in the dynamical case ofω≠0,the ac conductance oscillates with the amplitude e~2/h and the period which depends on the interaction strength and the driving frequency as well as the position in the wire.In the second part, we study theoretically the transport properties of an interacting quantum wire in the presence of a time-dependent point impurity.Using the Keldysh formalism within the framework of Luttinger-liquid model,we calculate and analyze the dc contribution of the backscattered current and the shot noise of the system with arbitrary Luttinger interaction strength and impurity position.From some numerical examples,we find that the time-dependent point impurity in the wire can enhance the total current in the strongly interaction regime,and the total current enhancement is dependent of the both impurity potential frequency and the equivalent frequency in relation to the drain-source voltage V.The dc contribution of the backscattered current oscillates as a function of impurity frequency with the period depending on the Luttinger interaction strength.Furthermore,the oscillation of the dc contribution of the backscattered current is not a finite-length effect,which is different from that in the case of system with a static point impurity, and the oscillation characteristic is also connected with V.However,the final current-noise relation is similar to that in the case of a static point impurity.In chapter four,we study the transport properties for a Luttingcr-liquid quantum wire in the presence of both Rashba spin-orbit coupling(SOC)and a weak external in-plane magnetic field.Generally,the ac conductivity is an oscillation function of the strengths of electron-electron interaction,Rashba SOC and magnetic field,as well as the driving frequency and the measurement position in the wire.Through analysis with some examples it is demonstrated that the modifica- tion on the conductivity due to electron-electron interactions is more remarkable than that due to SOC,while the effects of SOC and Zeeman splitting on the conductivity are very similar.The ratio of the spin-polarized conductivitiesσ_↑/σ_↑is dependent of the electron-electron interactions for the system without SOC, while it is independent of the electron-electron interactions for the system without Zeeman splitting.In chapter five,we study the alternative current(ac)transport properties for clean two-channel nonchiral and chiral Luttinger liquid systems with both interand intra-channel electron-electron interactions connected to two noninteracting reservoirs(leads).Using the bosonization technique within linear response theory, we have obtained the analytical expressions of the ac conductivity for the two types of LL systems,which are generally oscillation functions of the electron-electron interaction strengths,the ratio of Fermi velocities of the two channels, the driving frequency and the distance between the two different measurement positions in the reservoirs.The variation patterns of ac conductivity and their explanations are discussed by several numerical examples.Though the physics for the two types of LLs is expected to be quite different,but the ac conductivity has a similar variation pattern.However,the direct current(dc)conductance is reduced to quanta of 2e~2/h for nonchiral LL,while for chiral LL it is related to fractional quantum Hall conductance.In chapter six,we study theoretically the transport properties for a Luttinger liquid(LL)coupled to two Bose-Einstein condensation(BEC)reservoirs.Using the approach of equation of motion for the Green function of the system,we find that the distance between the two resonant transmission probability peaks of the system is determined by the bosonic interaction strengths,and the sharpness of these resonant peaks is mainly determined by the Rabi frequency and phase of the BEC reservoir.In chapter seven,a summary of the work and a outlook of this topic are given.