# Dresden 2014 – wissenschaftliches Programm

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# HL: Fachverband Halbleiterphysik

## HL 77: Frontiers of electronic structure theory - Non-equilibrium phenomena at the nano-scale V (organized by O)

### HL 77.3: Vortrag

### Mittwoch, 2. April 2014, 16:45–17:00, TRE Ma

**Quasiparticle self-consistent ***GW*** method with spin-orbit coupling applied to Bi and HgTe** — •Christoph Friedrich, Irene Aguilera, Markus Betzinger, and Stefan Blügel — Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany

We present an implementation of the quasiparticle self-consistent (QS) *GW*
method where the spin-orbit coupling (SOC) is fully taken into account in each
iteration rather than being added *a posteriori*. The implementation is based on the FLAPW method. The SOC gives rise to
spin off-diagonal blocks in the Green function *G*^{SOC} and the
self-energy Σ^{SOC}=*iG*^{SOC}*W*^{SOC}.
We applied the QS*G*^{SOC}*W*^{SOC} method to the semimetal Bi, which presents in experiment
small electron and hole pockets and a tiny band gap (11-15 meV) at the L point,
all of them largely overestimated by LDA (e.g., the gap is 86 meV). The QS*G*^{SOC}*W*^{SOC}
approach predicts a value of the band gap of 8 meV and electron and hole
pockets in very good agreement with experiment. The *a posteriori* treatment
of the SOC (QS*GW*+SOC), on the other hand, yields an unphysical result for Bi,
predicting it to be a topological insulator with a very large gap at L (260 meV)
instead of a trivial semimetal.
Similarly, for HgTe, QS*GW*+SOC reorders the bands in a wrong way and opens a gap at the Γ point in disagreement with experiment. In contrast, the QS*G*^{SOC}*W*^{SOC} approach yields a qualitatively and quantitatively correct description of the electronic band structure. We acknowledge support from the Helmholtz Association through the Virtual Institute for Topological Insulators (VITI).