Spectral and Fermi surface properties from Wannier interpolation

Abstract

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. Because of 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.

Toward a realistic description of multilayer black phosphorus: FromGWapproximation to large-scale tight-binding simulations

“…where Ω is the unit cell area, N k is the number of k points used for the Brillouin zone sampling, |mk is the Wannier-interpolated Bloch state [46], corresponding to the mth eigenvalue ε mk of the GW 0 Hamiltonian H GW0 k , f nk = exp(βε nk + 1) −1 is the Fermi-Dirac occupation factor involving the inverse temperature β, j α is the α component of the current operator, and η is a smearing parameter. The Brillouin zone was sampled by ∼10 7 and agation method [24,53], in which σ αβ (ω) is calculated conceptually similar to Eq.…”

“…To examine the fine structure of the electronic spectrum of monolayer BP, a denser mesh was considered. To obtain smooth band structures, densities of states and optical conductivities, we use an interpolation procedure by making use of the maximally localized Wannier functions [46][47][48], which are constructed by projecting the GW 0 Hamiltonian onto the entire manifold of the 3s and 3p states of phosphorus. For all the structures, we adopt experimental crystal structures of bulk BP [49] and introduce a vacuum layer of ∼15Å in order to minimize spurious effects due to the periodic boundary conditions in slab calculations.…”

EPW: A program for calculating the electron–phonon coupling using maximally localized Wannier functions

“…EPW therefore enables affordable, accurate, and extremely efficient calculations of the electron-phonon coupling [15]. The use of maximally localized Wannier functions (MLWFs) [16,17] to calculate Brillouin zone integrals with high accuracy has been the object of a number of other studies [18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Fröhlich Electron-Phonon Vertex from First Principles

“…The matrices U k are known at every point of the coarse grid from the calculation of maximally localized Wannier functions, and can be obtained at all other points via the interpolation of the electron Hamiltonian [41]. In order to demonstrate our approach we consider the electron-phonon coupling in a prototypical polar semiconductor, anatase TiO 2 .…”