PHYSICAL REVIEW B 88, 045206 (2013) GW study of topological insulators Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 : Beyond the perturbative one-shot approach Irene Aguilera, Christoph Friedrich, Gustav Bihlmayer, and Stefan Bl¨ ugel Peter Gr¨ unberg Institute and Institute for Advanced Simulation, Forschungszentrum J¨ ulich and JARA, D-52425 J¨ ulich, Germany (Received 25 June 2013; published 29 July 2013) We present GW calculations of the topological insulators Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 within the all-electron full-potential linearized augmented-plane-wave formalism. Quasiparticle effects produce significant qualitative changes in the band structures of these materials when compared to density functional theory (DFT), especially at the Ŵ point, where band inversion takes place. There, the widely used perturbative one-shot GW approach can produce unphysical band dispersions, as the quasiparticle wave functions are forced to be identical to the noninteracting single-particle states. We show that a treatment beyond the perturbative approach, which incorporates the off-diagonal GW matrix elements and thus enables many-body hybridization to be effective in the quasiparticle wave functions, is crucial in these cases to describe the characteristics of the band inversion around the Ŵ point in an appropriate way. In addition, this beyond one-shot GW approach allows us to calculate the values of the Z 2 topological invariants and compare them with those previously obtained within DFT. DOI: 10.1103/PhysRevB.88.045206 PACS number(s): 71.10.−w, 71.15.Mb, 71.20.−b, 71.70.Ej I. INTRODUCTION Recently, the concept of a new kind of insulator, the topological insulator, was developed. 1–5 This paved the way for new physics with new electronic phenomena and a great potential for applications in spintronics, quantum comput- ing, thermoelectrics, or Green IT, due to the possibility of generation and control of dissipationless spin currents. 6–8 In topological insulators, a strong spin-orbit interaction causes an inversion of electronic bands and gives rise to nontrivial edge or surface states that, by symmetry considerations, are required to be metallic. Moreover, the conducting edges and surfaces have several special features with respect to their transport properties. These conducting states realizing the metallic surfaces or edges are protected by time-reversal symmetry in the sense that electron propagation is dissipationless because the backscattering of charge carriers is forbidden as long as the topological properties are intact. 9 Among topological insulators, the family formed by Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 is one of the most widely studied due to the simplicity of their surface states consisting of a single Dirac cone at the Ŵ point. 10 Their experimental band gaps between 0.15 and 0.30 eV make them good candidates for experimental studies of topological effects and for room- temperature applications. In addition, these materials and some of their alloys are nowadays commonly used in thermoelectric refrigeration and power generation. 11,12 Most of the calculations present in the literature for this family of materials have been based on model Hamiltonians or parameter-dependent tight-binding descriptions, 1,13–15 and density functional theory (DFT) employing the local-density (LDA) or generalized gradient (GGA) approximations. 11,16–23 The LDA and GGA functionals, due to their efficiency, have allowed for the study of surface states of these materials. 10,24–27 However, these functionals are made for the electronic ground state, and it is known that they are not appropriate for band gaps and excited-state properties, such as the quasiparticle (QP) band structure. To overcome this problem, we employ many-body per- turbation theory in the GW approximation 28 to calculate quasiparticle self-energy corrections for the electronic states, which yields results that are directly comparable to pho- toemission spectroscopy measurements. Recently, GW cal- culations on Bi 2 Se 3 and Bi 2 Te 3 have shown 29–31 that not only a much better agreement of the band gap but also an improvement in the effective masses is found when com- paring to experimental results. We have performed one-shot GW calculations for Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 within the all-electron full-potential linearized augmented-plane-wave (FLAPW) method. The one-shot GW quasiparticle correction is usually applied in a perturbative approach, where the QP wave functions are approximated by the corresponding Kohn-Sham (KS) single-particle states, as this requires only the diagonal elements of the GW self-energy to be calculated. However, we demonstrate in this work that this leads to unphysical QP band dispersions, especially in regions of the Brillouin zone where hybridization is strongly affected by GW corrections as, for example, in the band-inverted region close to the Ŵ point. These unphysical dispersions are caused by the neglect of hybridization effects that arise from the off-diagonal part of the self-energy. In fact, going beyond the perturbative approach and thus allowing for changes in the QP wave functions immediately rectifies the band dispersions, which become smooth and physical. In addition, the inclusion of the off-diagonal elements of the self-energy allows us to obtain the GW quasiparticle wave functions and discuss properties derived from them, like the band inversion and the Z 2 topological invariants. 1,4 II. METHODSAND COMPUTATIONAL DETAILS All calculations were carried out within the all-electron FLAPW formalism as implemented in the DFT code FLEUR 32 and the GW code SPEX. 33 The FLAPW method treats core, valence, and conduction electrons on an equal footing. The electron density is determined self-consistently em- ploying the Perdew-Zunger parametrization of the LDA exchange-correlation functional. 34 The core electrons are 045206-1 1098-0121/2013/88(4)/045206(7) ©2013 American Physical Society