Electronic Transport Properties In Several Typical Quantum Waveguides

Quasi-one-dimensional mesoscopic structures can be referred as quantum waveguides, where the wave nature of electron in these structures must be considered, rather than to view it simply as a semiclassical particle. Thus, not only the amplitude but also the phase of the wavefunction of electron in quantum waveguides plays the important roles in determining the electron transport properties. In particular, the latter is the crucial quantity for the so-called quantum interference which is the interaction of the electron partial waves. It has been experimentally demonstrated that the most electron transport properties in quantum waveguides are dominated by the quantum interference. This is because that in quantum waveguides the decoherent scattering mechanisms, electron-phonon scattering for example, are weak or lacking. As a result, when the size of the quantum waveguide is comparable or smaller than electron phase relaxation length, the quantum interference of the electron waves remain. The scattering due to structure geometry and rigid impurities can only cause the finite phase shift, but not destroy the quantum interference. Therefore, the electron transport through the quantum waveguides is a coherent transmission process. To describe the electron transport through the quantum waveguides, a theoretical framework of quantum transport must be invoked.There are a variety of quantum waveguide structures. In the present thesis, within the Landauer-Buttiker formula and by means of the transfer matrix technique, we select several typical quantum waveguide structures to study the electron transport properties. These structures include a uniform quantum wire with square magnetic obstacles, the T-shaped two-terminal quantum waveguide, and graphene nanoribbons. The main outcomes of our investigation are as follows:First of all, for most quantum waveguide structures we investigate the common characters of the scattering matrix in details, based on the time reversal symmetry and probability current conversation. Furthermore, we prove the reversibility of the electron transmission probability amplitude, which is an indispensable relationship to formulate the electron transport properties in the quantum waveguide. Then, we discuss the relation between the scattering matrix and the transfer matrix. According to these results, we can finally establish the Landauer-Buttiker formula which is particularly adequate the quantum waveguide structures.Secondly, by means of the transfer matrix technique, we investigate the electronic transport through a quantum waveguide in the presence of a magnetic obstacle is investigated theoretically. A magnetic obstacle can be experimentally realized in quantum waveguide structures, for example, by doping dilute magnetic impurities, or by deposing a ferromagnetic material on the surface of a semiconductor heterostructure where the quantum waveguide is patterned. The difference of a magnetic potential from a conventional scattering potential lies in that an electron with a specific spin feels a barrier in the potential region whereas the electron with the opposite spin just feels a well. Therefore, the electrons with opposite spins present distinct transport behaviors when passing though a magnetic potential. By comparing the calculated conductance spectra of the opposite spin electrons, we find that there exists a notable spin filtering window in the low energy region. The dependence of such a spin filtering window on the size, position, and potential strength of the magnetic obstacle is studied in detail. Subsequently, we present a detailed investigation about the linear conductance spectrum in the quantum waveguide in the presence of two magnetic obstacles. The dependence of the linear conductance on the relative positions, the sizes, and the potential strength of the two obstacles is illustrated and discussed.Thirdly, we find that the so-called T-shaped quantum waveguide is a typical mesoscopic structure to exhibit the important role of quantum interference in the electronic transport process. In such a T-shaped quantum waveguide structure, the constructive quantum interference brings about the peaks in the conductance spectrum, which is called the resonant tunneling of the electron through the QD chain. On the contrary, the destructive quantum interference causes the zero points in the conductance spectrum, which is called the anti-resonant tunneling. We predict the positions of the resonant peaks and the anti-resonant points in the conductance spectrum, by using the noninteracting Anderson impurity model and Green function technique. The relevant conclusion is that when the energy of the incident electron coincides with the eigen-energy of the QD, namely the T-shaped region, the electron can tunnel resonantly to give a conductance peak; On the other hand, a conductance zero point occurs while the incident electron aligns its energy with the eigen-energy of the dangling QD. Although this conclusion is unambiguous and elegant, the theoretical model(the noninteracting Anderson impurity model) is too rough to describe quantitatively the electron transport properties in the multiple QD systems. Therefore, we calculate the linear conductance spectrum of an electron to pass though a quantum waveguide with a stub by means of the transfer matrix technique. Our result indicates that the positions of the resonant peaks and the antiresonant dips predicted by the Anderson impurity model are semi-quantitatively correct. To be specific, the both results from the Anderson model and the transfer matrix method agree well with each other about the resonant peaks. In contrast, finite deviations exist about the positions of antiresonant dips between the two approaches. In addition, we also display the possibility of the spin filtering by virtue of the T-shape quantum waveguide with a magnetic potential in the stub.Finally, we pay attention to the graphene nanoribbon, which is a new kind of quantum waveguide. Various Graphene nanoribbons becomes the current highlight in the mesoscopic physics since the experimental achievement of the graphene(a single atomic layer of graphite). Two typical structures consist of the armchair and zigzag graphene nanoribbons. For these two graphene quantum waveguides, we obtain the electron eigen-states analytically. In other words, we deal with the Dirac equation of electron in these two nanoribbons with the appropriate boundary conditions. The calculated energy band structure agrees well with the results of tight binding results. But the advantage of our treatment consists in that the wavefunctions of the eigen-states obtained by us have analytical forms. More importantly, we generalize the transfer matrix approach to the graphene nanoribbons by means of the time-reversal operator and the probability density operator unique to graphene, which can be used to investigate the electron transport properties in various graphene quantum waveguide structures, such as the zigzag graphene nanoribbon and some complicated quantum waveguides with inhomogeneous lateral structures.