Effects of various obstacles and tunneling disorder on the quantized conductance of an electron waveguide: Model of two coupled chains.

Abstract

The effect of various islandlike obstacles, placed inside an electron waveguide, and the disordered tunneling modulation on the quantized conductance is theoretically investigated with use of a model of two coupled chains. The Landauer-B\uttiker prescription, the tight-binding approximation, and the transfer-matrix method are used to calculate the conductance of this mesoscopic system. The islandlike obstacles with different shapes are described by different regular tunneling modulations in a finite active region. Both the propagating and evanescent modes in all the regions are taken into account in our calculations. The calculated results show that for these structures there are basic plateau structures in the conductance curve as a function of the Fermi energy. In addition, resonance structures are superimposed on the plateaus. However, the accuracy of the quantization and the resonance pattern in the conductance strongly depend on the interchannel tunneling modulations. The resonance structures in the conductance plateaus are smeared when the corresponding tunneling modulation alters smoothly over the obstacle region. We also study the variation of the quantized conductance with the Fermi energy for various multiply connected structures and for a system containing a finite-length obstacle with periodically modulated tunneling. A series of features in the conductance curve emerge. Roughness or corrugation always exists on the surfaces of the obstacles. This effect can be characterized by the randomly modulated tunneling between the two channels.In this work we also present the investigation of the influence of the tunneling disorder on the conductance. The effects of disordered interchain tunneling are threefold. First, it rounds the sharp corners of the quantization conductance. Second, it produces conductance fluctuations imposed on the plateaus. And third, the average value of the conductance is reduced by the interchain tunneling disorder. Both the localization length and the root-mean-square value of conductance fluctuations depend on the extent of disorder and the Fermi energy. We also present the statistical distribution of conductance fluctuations in this disordering system. It is found that the statistical distribution can be normal, log-normal, or neither the former nor the latter, depending on the extent of disorder and the Fermi energy. Finally, we have studied the combined effect of both the site-energy disorder and the tunneling disorder on the conductance. We find that the two disorders are of a very similar nature. In summary, we conclude that this two-coupled-chain model is shown to describe the essence of quantum ballistic transport of electrons in a nonuniform electron waveguide with two channels in a simple and transparent way.