Maximally-localized Wannier functions for GW quasiparticles

We review the formalisms of the self-consistent GW approximation to many-body perturbation theory and of the generation of optimally-localized Wannier functions from groups of energy bands. We show that the quasiparticle Bloch wave functions from such GW calculations can be used within this Wannier framework. These Wannier functions can be used to interpolate the many-body band structure from the coarse mesh of Brillouin zone points on which it is known from the initial calculation to the usual symmetry lines, and we demonstrate that this procedure is accurate and efficient for the self-consistent GW band structure. The resemblance of these Wannier functions to the bond orbitals discussed in the chemical community led us to expect differences between density-functional and many-body functions that could be qualitatively interpreted. However, the differences proved to be minimal in the cases studied. Detailed results are presented for SrTiO_3 and solid argon.

Fermi-surface calculation of the anomalous Hall conductivity

While the intrinsic anomalous Hall conductivity is normally written in terms of an integral of the electronic Berry curvature over the occupied portions of the Brillouin zone, Haldane has recently pointed out that this quantity (or more precisely, its ``non-quantized part) may alternatively be expressed as a Fermi-surface property. Here we present an {it ab-initio} approach for computing the anomalous Hall conductivity that takes advantage of this observation by converting the integral over the Fermi sea into a more efficient integral on the Fermi surface only. First, a conventional electronic-structure calculation is performed with spin-orbit interaction included. Maximally-localized Wannier functions are then constructed by a post-processing step in order to convert the {it ab-initio} electronic structure around the Fermi level into a tight-binding-like form. Working in the Wannier representation, the Brillouin zone is sampled on a large number of equally spaced parallel slices oriented normal to the total magnetization. On each slice, we find the intersections of the Fermi-surface sheets with the slice by standard contour methods, organize these into a set of closed loops, and compute the Berry phases of the Bloch states as they are transported around these loops. The anomalous Hall conductivity is proportional to the sum of the Berry phases of all the loops on all the slices. Illustrative calculations are performed for Fe, Co and Ni.