Positive Hall Coefficients of Non-Magnetic and Non-Crystalline Metals

本文根据伊藤的霍尔电导率严格公式，对传统的紧束缚处理霍尔效应的Peierls近似进行了检验。结果表明，Peierls相与公式中的经典路径完全对应，当考虑非经典路径时，电子-空穴对称性得到恢复。我们引入了“三次矩阵表示”，它将顶点函数的积分方程映射为一维形式。根据Harrison的固体状态表，电导率与实验结果符合得很好，但在计算中忽略了s-和p-轨道之间的对称性差异，这对霍尔效应是必不可少的。为了处理足够大的系统，从而使不可避免的外推更可靠，我们开发了一种新的数值方法，大大加快了计算速度。它几乎等于用解析的方法来处理绿色函数的时间演化，其惊人的数值精度已被电子结构的模型计算所证明。目前正在将其应用于运输。

The traditional Peierls approximation in the tight-binding treatment of the Hall effect has been examined in the light of Itoh's rigorous formula for the Hall conductivity. It was confirmed that the Peierls phase corresponds exactly to the classical path in the formula, and that the electron-hole symmetry is recovered when including non-classical paths.A mean-field theory of transport has been attempted for liquid 3d-transition metals. We introduced "cubic matrix representation", which maps the integral equations for the vertex functions into one-dimensional forms. According to Harrison's Solid State Table, a good agreement with experiment resulted for the conductivity, but the symmetry difference between s- and p-orbitals neglected in this calculation was found to be essential for the Hall effect. We further plan to continue the work by including p-orbitals.For dealing with sufficiently large systems, and thus making the unavoidable extrapolation more reliable, we developed a new numerical method that accelerates the computation dramatically. It tantamounts to treat the time evolution of the Green function analytically, and its amazing numerical accuracy has been exemplified by model calculations for electronic structures. Its application to the transport is now under way.