Influence Of Scattering Impurities On Transport Properties Of Two-Dimensional Electron Systems

Mesoscopic physics has been developed a branch of physics from the eighties in the twentieth century. Mesoscopic system is the one whose scale is between the macro-and micro-scale. Its physical phenomena can be observed explicitly showing the effects of quantum phase coherence. Therefore, from the physical sense, the scale of mesoscopic systems is close to the phase coherence length. The study of physical problems is caused by quantum coherence in the narrow objects, which forms a subject named "mesoscopic physics" .Once the electronic devices being in the scale of mesoscopic systems, we have to consider the coherence of the electron in the study of electron transport. Quantum coherent transport is universal in mesoscopic systems. At low temperatures, mesoscopic systems show a lot of quantum effects and phenomena. For example, the quantization conductance, universal conductance fluctuation, conductance changing with the magnetic field which shows by magnetic fingerprints. Conductance quantization is the most one of important physical phenomena. These phenomena play an important role on the validation of quantum mechanics and design of new electronic devices. It has been widespread concern in physics workers because of its scientific significance and potential practical value. Firstly, in this artical, we briefly introduced mesoscopic physics, and Landauer-Buttiker transport theory which is the most commonly method used in mesoscopic physics. At zero-temperiture, we derive the conductance formula at both ends for the single-channel and the multi-channel situation, as well as the influence of temperiture on the conductance. A brief description of the peculiar quantum effects and phenomena of mesoscopic physics, as well as its potential scientific significance and application value, are disscussed.Secondly, we use transfer matrix theory to study the electron wave transport problems of a two-dimensional system which contains one finite-size scattering impurity. At zero temperiture, when the size of system and scattering impurity are determined, conductance shows the quantum phenomina of stepped, which increases with the incresing of Fermi wave vector of the incident electron; When the size of system and the energy of incident electron are determined, conductance also shows the quantum phenomina of stepped increasing with the decrese of the width of scattering impurity. Periodic oscillation with the incresing of the length of scattering impurity is given. When the size of system and scattering impurity and the energy of incident electron were determined, conductance decreases with the incresing of the temperiture. At nano-zero temperiture, when the size of system and scattering impurity are determined, conductance also shows the quantum phenomina of stepped, which increases with the incresing of Fermi wave vector of the incident electron, as well as the step becomes some silt.Thirdly, we use scattering matrix theory to study the electron wave transport problems of a two-dimensional system which contains one finite-size scattering impurity. When the length of scattering impurity is large, transfer matrix theory leds to the difficulty in the calculation of index of divergence. While scattering matrix theory avoided this difficulty, the results obtain by scattering matrix theory are more accurate than the transfer matrix theory.At last, we use scattering matrix method to study the electron wave transport problems of a two-dimensional system which contains many finite-size scattering impurities. When the system contains many finite-size scattering impurities, conductance also show the quantum phenomina of stepped increases. However, there is a clear oscillation on the rise.