Regensburg 2013 – wissenschaftliches Programm
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MA: Fachverband Magnetismus
MA 50: Poster II
MA 50.62: Poster
Freitag, 15. März 2013, 10:30–13:30, Poster D
Efficient integration method for the intrinsic anomalous Hall conductivity — •Alexander Mook1, Falko Pientka1,2, Ingrid Mertig1,3, and Peter Zahn1,4 — 1Institut für Physik, Martin-Luther-Universität, Von-Seckendorff-Platz 1, D-06120 Halle — 2Fachbereich Physik, Freie Universität, D-14195 Berlin — 3Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle — 4Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden
Haldane has already presented the expression of the intrinsic anomalous Hall conductivity as an integral over the Fermi surface as expected for Fermi-liquid theory [1] replacing the volume integral of the occupied states in the Brillouin zone.
We implemented both integration methods and applied them to a 4-band (sp3) tight-binding Hamiltonian including both exchange splitting and spin-orbit coupling. Furthermore, we used an adaptive tetrahedral mesh refinement being based on the 8-tetrahedra-shortest-interior-edge method [2] to obtain convergence when integration over avoided crossings is necessary. Our investigations show that the results of both methods agree very well.
The adaptive integration method is applicable to advanced ab initio electronic structure schemes which provide besides the band energies also the Berry curvature.
[1] F. D. M. Haldane, Phys. Rev. Lett. 93, 206602 (2004). [2] S. Zhang, Houston J. Math. 21 (3), 541-556 (1995).