Anisotropic Transport for Parabolic, Non-Parabolic and Linear Bands of   Different Dimensions
  Anisotropic thermoelectrics is a very interesting topic among recent research. The transport distribution function plays the central role on modeling the anisotropic thermoelectrics. The methodology of numerical integrations is used in previous literature on anisotropic transport, which does not capture the sharp change of transport distribution function and density of states at band edges. However, the sharp change of transport distribution function and density of states at band edges plays the central role in enhancing the thermoelectric performance. Thus, an analytical methodology that is robust on modeling the sharp change of transport distribution function and density of states at a band edges is needed. To our best knowledge, there has not been a paper giving the systematic study on the analytical models of anisotropic transport distribution function for different kinds of band valleys in different dimensions under different assumptions. Therefore, the main focus of this present paper is to develop such a robust analytical methodology on modeling the anisotropic transport distribution function. So our contributions are 1) we have developed a systematic method on model the anisotropic transport distribution function, for 3D, 2D and 1D systems, in parabolic, non-parabolic and linear dispersion relations, under both the relaxation time approximation and the mean free path approximation; 2) we have found that the Onsage's relation of transport can be violated under certain conditions; 3) we have compared our newly developed methodology with the traditional used numerical methodology. 
Shuang Tang, Mildred Dresselhaus
cond-mat.mtrl-sci