在凝體物理中絕大多數金屬導體的傳輸性質是由系統的弛豫時間(relaxation time)所決定的。最近幾年有一系列新的材料他們的傳輸性質不僅是由弛豫時間所決定，材料的能帶結構的拓樸性質也扮演著很重要的腳色。而外爾半金屬(Weyl semimetal)就是其中一類的拓樸材料。在這論文裡我們想要研究的是像外爾半金屬這類的拓樸材料，它們的拓樸性質是否也會反映在它們的熱傳導和熱電效應上。在本文中我們透過波茲曼方程式(Boltzmann equation)和線性化的能帶結構用半古典的方式去計算外爾半金屬中的傳輸性質，並與久保公式(Kubo formula)的結果作比較。外爾半金屬的異常傳導性質來自於能帶結構中的外爾點(Weyl node)的特殊拓樸，我們希望能了解這類能帶拓樸性質是否也會反映在材料的熱傳導以及熱電效應上。
在我們的結果中發現，熱傳導和熱電效應中並沒有明顯的異常現象發生。另外我們用久保公式研究Thermal Chiral Magnetic effect發現，系統中並沒有類似的傳導現象出現。

In most of conductors, the transport properties are governed by the relaxation time of the material. Recently, there is new kind of material that its transport is not only determind by the relaxation time but also the topology of band structure. The Weyl semimetal is one of these topological materials. In this thesis, we investigate the electronic and thermal transport properties of the Weyl semimetal based on Boltzmann equation approach and a linearized Weyl semimetal model. We also compare the result of Boltzmann equation to the Kubo formula approach. The anomalous electronic transport properties of the Weyl semimetal are originated from the topology of Weyl nodes. We expect that the analogous effect can also be found in the thermal transport and electric effect of Weyl semimetal.
Our result shows that while anomalous behavior shows up in electronic transport, thermal conductivity and thermoelectric properties may not have the similar behavior under parallel electric field and magnetic field. On the other hand, by studying the Kubo formula approach we found that there is no thermal chiral magnetic effect.

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