Researches On Acoustic Phonon Transmission And Thermal Conductivity In Low-Dimensional Quantum Structures

Landauer's work in the late 50s initiated the exploration of the nature of quantum transport. The physics of electron transport in one dimension has attracted a great deal of attention during the last two decades. Recently, the low-temperature heat transport in a mesoscopic dielectric system in which the wavelength of thermal phonons can be comparable to the geometrical size of the system has attracted much attention both experimentally and theoretically. In this thesis, we mainly investigate the acoustic phonon transmission and thermal conductance in quantum wire.Using the scattering-matrix method, we investigate the influences of boundary conditions on thermal conductance in quantum wire with structural defect. A comparison between the thermal conductance is made when stress-free, hard-wall, and mixed boundary conditions are applied for acoustic transport leads. The results show that the quantized thermal conductance plateau at very low temperature can be observed only in transport lead with stress-free boundary condition. For hard-wall or mixed boundary conditions, qualitatively different thermal conductance characteristics are found. Moreover, we find that the behavior of the thermal conductance sensitively depend on the geometric parameters and the position of the defect in quantum wire.Considering this kind of structure being proposed that should exhibit large oscillations in a magnetic or in an electric field, we investigate the acoustic phonon transmission and thermal conductance in a multiple channels nanostructure at low temperature using the scattering-matrix method. Our results show that phonon transport are strongly influenced by mode coupling effect between channels, and the effect is different for different types of boundary conditions between channels. We also find that the transmission spectra show a staircaselike behavior with large oscillation, and an abrupt jump is always located just at an integer-reduced frequency.The influence of coupled-defect on the thermal conductance in quantum wire was investigated based on the scattering-matrix method. Three types of coupled-defect are employed in our calculation. We present a detailed study of the thermal conductance as a function of distance between two defects and temperature. The results show that there is qualitative difference in the dependence of the thermal conductance versus width between two defects for different temperature. We also find that the calculated thermal conductance increase with the width W of quantum wire in all cases. Finally, in order to investigate the heat transport of various nanostructure, we study the effect of the shapes of the cross section of three-dimensional nanowire on phonon transport and thermal conductance at low temperature. A comparison between the thermal conductance is made when three-dimensional nanowire and two-dimensional nanowire used in our calculation. It is found that increasing the anisotropy of the cross section results in a decrease of the values of the conductance . We also find that phonon transmission and thermal conductance in three-dimensional nanowire are not in agreement with that in two-dimensional nanowire.