Electronic Transport Properties In Quantum Waveguides

As the developing of material growth techniques , such as molecular beam epitaxy and electron-beam lithography ,etc , People have obtain various low-dimensional semiconductor-base devices such as superlattice and heterojunction . As the size of the semiconductor devices is similar to the de Broglie wavelength of the electron, particles in those structures follow the rule of quantum mechanics, and therefore many new properties are observed which are hard to be seen in bulks. As new phenomenons being observed and new theories and models being raised, the study of these structures has developed into a new branch of condense physics which is called mesoscopic physics. Quasi-one-dimensional mesoscopic structures can be regarded as quantum waveguide, where the wave nature of electron in these structures must be considered. 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. Therefore, instead of the classic theories of transport, we should use quantum mechanics theories to study these structures. In this thesis, we mainly use the theory of Landauer Büttiker to study the electron transport properties in quantum waveguide.The key of using Landauer Büttiker theory to study electron transport properties is to obtain transmission probability and reflection probability of the scattering region, and there are several different ways we can tackle this problem such as: Transfer matrix method, Scatter matrix method, Mode matching method and Green function. We introduce the basic of those methods and, according to the structures, we will use different method to solve this problem.First of all, we focus on the semiconductor quantum waveguide with magnetic obstacles in it. 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. In this thesis we mainly discuss the effect of magnetic obstacle on electronic transport properties. And we have conclusion as follow:(1) To a very simple model, the step model, we propose a common method to calculate the transfer matrix in details, based on the time reversal symmetry and probability current conversation. Furthermore, we calculate the scatter matrix from transmit matrix. In the end, we can finally establish the Landauer Büttiker formula which is particularly adequate the quantum waveguide structures.(2) We investigate the electronic transport properties of the quantum waveguide with a single magnetic obstacle in it. And we use the method of transport matrix as we introduced before. The model that we discuss is a waveguide with a square magnetic obstacle in it. To the electron with up-spin it feel a potential barrier, on the other hand the electron with down-spin it feel a potential well. To this model , we found that the electrons with different spin don't have the same transmission probability. And 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. Furthermore, The dependence of such spin filtering window on the size, position, and potential strength of the magnetic obstacle is studied in detail. And we believe it will be a useful spin control device.(3) We present a detailed investigation about the linear conductance spectrum in the quantum waveguide in the presence of two magnetic obstacles. First we establish the transfer matrix for the quantum waveguide in the presence of two magnetic obstacles. Then calculate the conductance spectrum which shows that the oscillation of two magnetic obstacles is more complex. There are two different kind of formant. The spectrum of electron with up-spin shows Breit-Winger formant. And the spectrum of electron with down-spin shows Fano formant. We analyze the cause of the different. Then, we investigate the dependence of the linear conductance on the relative positions, the size, and the potential strength of the two obstacles. And we discuss the formant illustrated in spectrum in details. (4) We introduce the Mode matching method into quantum waveguide, and use it to solve the problem of many magnetic obstacles. We consider transport in a quantum waveguide with a linear array of square magnetic obstacles in it. First we investigate transport in a quantum waveguide with two square magnetic obstacles in it, and comparing with the conclusion obtained before. Then, the dependence of conductance on the number of magnetic obstacles is discussed in details. We find to choose particular number of magnetic obstacles and Fermi energy we will control electronic efficiently.Finally, we pay attention to the grapheme nanoribbon, which is a new kind of quantum waveguide. Various graphene nanoribbons become the current highlight in the mesoscopic physics since the experimental achievement of the graphene. We focus on the conductance of the L type nanoribbon. We illustrate the conductance spectra with different shape in detail, and compare the conductance spectra with energy band spectra. We analyze the dependence of conductance on the energy band.