Many‐Body Effects in the Electronic Structure of Topological Insulators

Abstract

IntroductionMost of the calculations present in the literature for topological insulators (TIs) are based on model Hamiltonians or parameter-dependent tight-binding descriptions [1][2][3][4], and density functional theory (DFT) employing either the local density approximations (LDA) or generalized gradient approximations (GGA) [5][6][7][8][9][10][11][12][13]. Because of their efficiency, the LDA and GGA functionals have allowed for the study of surface and edge states of these materials [14][15][16][17][18][19], and they have shown mostly good agreement with the experimental results. However, LDA and GGA are approximations to the ground-state energy and cannot in principle be expected to yield accurate excited-state properties. More specifically, one often takes the single-particle states that solve the Kohn-Sham (KS) equation of DFT as approximate excitations energies. But these states, strictly speaking, are merely mathematical tools that cannot be endowed with a physical meaning. In particular, they suffer from a strong self-interaction error and lack many-body renormalization effects. Related to that, the DFT bandgap of insulators and semiconductors, though in fact being a ground-state property, is systematically underestimated [20][21][22]. TIs are not an exception: because of their inverted bandgaps, the DFT underestimation of the bandgaps has not only quantitative but also qualitative consequences, and it can even lead to the wrong prediction of some trivial insulators as TIs [23]. Recently, to overcome this problem, calculations [23-33] based on the approximation [34] for the self-energy have started to emerge in the theoretical study of TIs and have shown that not only a much better agreement of the bandgap (in nature and magnitude) but also an improvement in the effective masses and spin-orbit splittings is found when compared to experimental results.In TIs, a strong spin-orbit coupling (SOC) causes the top valence and the bottom conduction band to invert in the bandgap region. The bands hybridize so that an energy gap forms that is of the order of the spin-orbit strength (up to a few hundreds of millielectronvolts). Such small bandgaps require a reliable description of the electronic structure. The inverted band structure is often -but not always, Topological Insulators: Fundamentals and Perspectives, First Edition. Edited

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“…Topological insulators commonly contain heavy elements (Se, Te, Bi, Sb) and depend on spin-orbit coupling for band inversion (Aguilera et al, 2013a,b, 2015a; Nechaev and Chulkov, 2013; Nechaev et al, 2015). For a detailed review of GW +SOC calculations, see Aguilera et al (2015b). To describe spin-dependent interactions between particles, one must generalize Hedin's equations beyond the Coulomb interaction, which has no spin dependence.…”

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“…Topological insulators commonly contain heavy elements (Se, Te, Bi, Sb) and depend on spin-orbit coupling for band inversion (Aguilera et al, 2013a(Aguilera et al, ,b, 2015aNechaev et al, 2015;Nechaev and Chulkov, 2013). For a detailed review of GW +SOC calculations, see Aguilera et al, 2015b. To describe spindependent interactions between particles, one must generalize Hedin's equations beyond the Coulomb interaction, which has no spin dependence. This generalization was recently completed Biermann, 2008, 2009) and allows one to treat magnetic dipoledipole interactions, for example.…”