A non-iterative method for vertex corrections of the Kubo formula for electric conductivity

Abstract

When computing electric conductivity based on the Kubo formula, vertex corrections describe such effects as anisotropic scattering and quantum interference and are important in determining quantum transport properties. These vertex corrections are obtained by solving the Bethe–Salpeter equation, which can become numerically intractable when a large number of k-points and multiple bands are involved. We introduce a non-iterative approach to vertex correction based on rank factorization of the impurity vertices, which significantly alleviates the computational burden. We demonstrate that this method can be implemented along with effective Hamiltonians extracted from electronic structure calculations on perfect crystals, thereby enabling the quantitative analysis of quantum effects in electron conduction for real materials.