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

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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.