Research On Thermal Transport In Low-dimension Quantum System

Recently, with the rapid devlepment of micro-/nano-fabrication techniques, the feature sizes of electronic device and thermal pathway are scaling down to nanodimenssion. There has increasing attention to nano-dimenssional electronic device due to their novel physical properties and extensive application prospects. The study of low-dimensional quantum system and correlative work has been a very important development direction of condensed. matter physics and study embranchment of new technology and new devices, which plays a crucial role in new and high-tech domain. In this paper, we investigate the property of quantum thermal conductance in low-dimensional quantum system and the influence for nanostructure dimension to thermal transport widely, and we find some significative results.Ballistic thermal conductance in a three-dimensional quantum wire with a stub structure is presentedunder both stress-free and hard wall boundary conditions at low temperatures. A comparative analysis for two-dimensional and three-dimensional models is made. The results show that whenstress-free boundary conditions are applied, the universal quantum thermal conductance can beobserved regardless of the geometry details in the limit T→0, and the behavior of the thermalconductance is qualitatively similar to that calculated by two-dimensional model. However, when hard wall boundary conditions are applied, the thermal conductance displays different behaviors inboth two-dimensional and three-dimensional models.Using scattering-matrix method,ballistic thermal transport properties at low temperatures in a quantum wire modulated withtwo coupling quantum dots are studied. The results show that when the temperature is low enoughwhere only the lowest mode can be excited, the reduced thermal conductance displays monotonicbehavior with the change of structural parameters. At higher temperature, more modes can beexcited and the reduced thermal conductance displays a nonlinear behavior with the change of thestructural parameters. It is also found that the phonon transmission and thermal conductance sensitively depend on the relative position of quantum dots and symmetric axis of the quantumwire. When the symmetry axis of quantum wire is away from the center of the quantum dots, thethermal conductance increases monotonously, and is different when the symmetric axis of quantumwire is away from from the center of quantum dot along different routes. It is also found that the thermal conductance can be modulated by the magnitude of the quantum dots and the length between the two quantum-dots. Moreover, inhomogeneous quantum transport steps and quantizedthermal conductance plateau can be observed in such structure.In the previous work, our studies foucs on the thermal transport of only single vibrational mode. Actually, the quantum thermal conductance relies on four low-lying acoustic vibrational modes. The thermal conductance associated with the lowest six types of ballistic phonon modes in quantum wire with catenoidal contacts is investigated. The results show that the cutoff frequency for the four types of acoustic modes is zero, while two types of optical modes are of nonzero cutoff frequency. For a perfect quantum wire, a quantized thermal conductance plateau can be observed. While for the structure with catenoidal contacts, the thermal conductance plateau is broken and a decrease in thermal conductance appears. The results also show that the reduced thermal conductance contributed from different vibrational modes has different characteristics.The ballistical phonon transport and thermal conductance of the six low-lying vibration modes at low temperatures in quantum wire modulated with quantum dot is investigated. A comparative analysis for the thermal conductance for the six vibrational modes is made. The results show that the transmission possibility of the six vibrational modes displays periodic or quasi-periodic oscillatory behavior. The thermal conductance contributed by different vibrational modes is of different characteristics, and can be adjusted by changing the structural parameters of the quantum dot.Moreover, we investigate the influence for five kides of scattering mechanisms to thermal conductivity, which are three-phonon Umklapp scattering, boundary scattering, interfacial scattering, mass difference(impurities) scattering, and phonon-electron scattering. Among the five kides of scattering mechanisms, the boundary scattering and the interfacial scattering are dominant resistive process for the decrease of the thermal conductivity. It is effective to adjust thermal conductivity by changing the dimension of the cross-section and the thickness of the constituent layers of the unit cell of the superlattice. The study also shows that the group velocity of phonons is dependent on the dimension of the cross-section, which can change the thermal conductivity effectively.