NASA Developmental Biology Workshop: A summary

The Life Sciences Division of the National Aeronautics and Space Administration (NASA) as part of its continuing assessment of its research program, convened a workshop on Developmental Biology to determine whether there are important scientific studies in this area which warrant continued or expanded NASA support. The workshop consisted of six panels, each of which focused on a single major phylogenetic group. The objectives of each panel were to determine whether gravity plays a role in the ontogeny of their subject group, to determine whether the microgravity of spaceflight can be used to help understand fundamental problems in developmental biology, to develop the rationale and hypotheses for conducting NASA-relevant research in development biology both on the ground and in space, and to identify any unique equipment and facilities that would be required to support both ground-based and spaceflight experiments

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.Comment: 12 pages, 9 figure