# Solid State Physics Seminar/iNANO foredrag - Irene Aguilera: 'Ab-initio methods for topological insulators'

**Irene Aguilera**

**Forschungszentrum Jülich**

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**Ab-initio methods for topological insulators.**

In topological insulators, the spin-orbit interaction leads to a band inversion and to nontrivial edge or surface states, which reside in the energy gap of the bulk material and are protected by time-reversal symmetry. Most of the ab-initio calculations present in the literature for these materials are carried out within density-functional theory (DFT) employing the local-density (LDA) or generalized gradient approximation (GGA), which can describe the ground-state properties accurately but are not appropriate for band gaps and excited-state properties, such as the quasiparticle energies. To overcome this problem, one can use the GW and quasiparticle self-consistent GW (QSGW) approximations to calculate quasiparticle corrections for the electronic states. This yields results that are directly comparable with photoemission spectroscopy measurements. I will introduce these approaches and discuss the importance of the spin-orbit coupling (SOC) being fully taken into account, instead of being added a posteriori, as in most GW calculations in the literature.

We have performed GW calculations for bulk Bi2Se3, Bi2Te3, and Sb2Te3 [1-3], and mercury chalcogenides [4], within the all-electron FLAPW formalism [www.flapw.de]. Results are in better agreement with experiments than the LDA ones [3-4]. We have also applied the QSGW method to bismuth and HgTe. Bismuth is a topologically trivial semimetal, which presents small electron and hole pockets and a tiny band gap at the L point (11-15 meV), largely overestimated by LDA (86 meV). Our QSGW calculation predicts a value of the band gap of 8 meV and the overlap between the electron and hole pockets in very good agreement with experiments.

We also show that spin-orbit coupling has to be fully taken into account in QSGW in order to obtain physical results for Bi and HgTe. For bismuth, the most widely used "a-posteriori" treatment of SOC predicts it to be a topological insulator with a too large gap at L (260 meV), instead of a trivial semimetal. For HgTe, this treatment of SOC produces unphysical results, reordering the bands in a wrong way and opening a gap at the Gamma point in complete disagreement with experiments. We show that, in contrast, when QSGW calculations are performed taking fully into account SOC, results for HgTe and Bi are qualitatively and quantitatively in very good agreement with experiments. In view of these results, we also use the QSGW approach to study the trivial-to-topological transition that bulk bismuth experiences under strain.

[1] I. Aguilera, C. Friedrich, G. Bihlmayer, and S. Blügel, Phys. Rev. B 88, 045206 (2013)

[2] I. Aguilera, C. Friedrich, S. Blügel, Phys. Rev. B 88, 165136 (2013)

[3] I. A. Nechaev et al., Phys. Rev. B 87, 121111 (2013)

[4] R. Sakuma, C. Friedrich, T. Miyake, S. Blügel, and F. Aryasetiawan, Phys. Rev. B, 84, 085144 (2011)

Dr. Irene Aguilera

Quantum Theory of Materials

Peter Gruenberg Institut (PGI-1)

Forschungszentrum Juelich

(Geb. 04.8 R. 240)

D-52425 Juelich

**Host:** Philip Hofmann, iNANO & Department of Physics and Astronomy, Aarhus University.

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