2007/02/23 by Jonathan R. Yates, Xinjie Wang, David Vanderbilt +1 · 6 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic orbital #Classical mechanics #Electron #Electronic structure #Hamiltonian (control theory) #Interpolation (computer graphics) #Magnetic properties of thin films #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Surface and Thin Film Phenomena #Tight binding #Wannier function #cond-mat.mtrl-sci
paper · pdf · doi:10.1103/physrevb.75.195121
12 pages, 7 figures
arxiv created 2007/02/23 · openalex publication_date 2007/05/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present an efficient first-principles approach for calculating Fermi surface averages and spectral properties of solids, and use it to compute the low-field Hall coefficient of several cubic metals and the magnetic circular dichroism of iron. The first step is to perform a conventional first-principles calculation and store the low-lying Bloch functions evaluated on a uniform grid of k points in the Brillouin zone. We then map those states onto a set of maximally localized Wannier functions, and evaluate the matrix elements of the Hamiltonian and the other needed operators between the Wannier orbitals, thus setting up an ``exact tight-binding model.'' In this compact representation the k-space quantities are evaluated inexpensively using a generalized Slater-Koster interpolation. Owing to the strong localization of the Wannier orbitals in real space, the smoothness and accuracy of the k-space interpolation increases rapidly with the number of grid points originally used to construct the Wannier functions. This allows k-space integrals to be performed with ab initio accuracy at low cost. In the Wannier representation, band gradients, effective masses, and other k derivatives needed for transport and optical coefficients can be evaluated analytically, producing numerically stable results even at band crossings and near weak avoided crossings.