To obtain an effective many-body model of graphene and related materials from first principles we calculate the partially screened frequency dependent Coulomb interaction. In graphene, the effective on-site (Hubbard) interaction is U00 = 9.3 eV in close vicinity to the critical value separating conducting graphene from an insulating phase emphasizing the importance of non-local Coulomb terms. The nearest-neighbor Coulomb interaction strength is computed to U01 = 5.5 eV. In the long wavelength limit, we find the effective background dielectric constant of graphite to be ǫ = 2.5 in very good agreement with experiment.

The effective on-site Coulomb interaction (Hubbard U ) between localized d electrons in 3d, 4d, and 5d transition metals is calculated employing a parameter-free realization of the constrained random-phase approximation using Wannier functions within the full-potential linearized augmented-plane-wave method. The U values lie between 1.5 and 5.7 eV and depend on the crystal structure, spin polarization, d electron number, and d orbital filling. On the basis of the calculated U parameters, we discuss the strength of the electronic correlations and the instability of the paramagnetic state toward the ferromagnetic one for 3d metals. 3 However, in these models the Coulomb and also the one-particle hopping matrix elements are typically empirical parameters that are determined such that the employed model reproduces experimental results of interest.For a long time, DFT-LDA and many-body model Hamiltonian methods have been separate and complementary approaches. This has drastically changed with the advent of the dynamical mean-field theory (DMFT), 4 which merged with the LDA to become a novel computational method referred to as LDA + DMFT, 5 which developed into a modern many-body approach for treating correlated electron materials. In retrospect, the so-called LDA + U method, 6 an early attempt to correct the LDA functional by introducing a simple mean-field-like Hubbard U term for localized d or f states, and today routinely applied to a broad spectrum of systems, can be regarded as its static limit. Both LDA + U and LDA + DMFT as well as other approaches not mentioned here rely on the Hubbard U as an additional parameter. Frequently, the exact value of U is unknown, which impedes the predictive power of these approaches.The problem of calculating the parameter-free Hubbard U for transition metals (TMs), i.e., from first principles, has been addressed by several authors.7-11 A number of different approaches have been proposed. Among them, the constrained local-density approximation (cLDA) 9 is the most popular. However, the cLDA is known to give unreasonably large U values for late TMs due to difficulties in compensating for the self-screening error of the localized electrons.10 Furthermore, the frequency dependence of U is unattainable. On the other hand, the constrained random-phase approximation (cRPA), though numerically much more demanding, does not suffer from these difficulties. In contrast to the cLDA, it also allows access to individual Coulomb matrix elements, e.g., on-site, off-site, intra-orbital, interorbital, and exchange.The aim of this Rapid Communication is to present a systematic study of the effective on-site Coulomb interaction (Hubbard U) between localized d electrons in TMs determined by means of first-principles calculations. Previous cRPA studies of U in TMs have focused only on the nonmagnetic (NM) state of the 3d series, and the results appeared to be strongly dependent on the parameters used in the cRPA schemes. 10,11 In the present work, we propose an alternative simple parameter-free c...

We present an implementation of the GW approximation for the electronic self-energy within the full-potential linearized augmented-plane-wave (FLAPW) method. The algorithm uses an allelectron mixed product basis for the representation of response matrices and related quantities. This basis is derived from the FLAPW basis and is exact for wave-function products. The correlation part of the self-energy is calculated on the imaginary frequency axis with a subsequent analytic continuation to the real axis. As an alternative we can perform the frequency convolution of the Green function G and the dynamically screened Coulomb interaction W explicitly by a contour integration. The singularity of the bare and screened interaction potentials gives rise to a numerically important self-energy contribution, which we treat analytically to achieve good convergence with respect to the k-point sampling. As numerical realizations of the GW approximation typically suffer from the high computational expense required for the evaluation of the nonlocal and frequencydependent self-energy, we demonstrate how the algorithm can be made very efficient by exploiting spatial and time-reversal symmetry as well as by applying an optimization of the mixed product basis that retains only the numerically important contributions of the electron-electron interaction. This optimization step reduces the basis size without compromising the accuracy and accelerates the code considerably. Furthermore, we demonstrate that one can employ an extrapolar approximation for high-lying states to reduce the number of empty states that must be taken into account explicitly in the construction of the polarization function and the self-energy. We show convergence tests, CPU timings, and results for prototype semiconductors and insulators as well as ferromagnetic nickel.

Using angle-resolved photoelectron spectroscopy and ab-initio GW calculations, we unambiguously show that the widely investigated three-dimensional topological insulator Bi2Se3 has a direct band gap at the Γ point. Experimentally, this is shown by a three-dimensional band mapping in large fractions of the Brillouin zone. Theoretically, we demonstrate that the valence band maximum is located at the Γ point only if many-body effects are included in the calculation. Otherwise, it is found in a high-symmetry mirror plane away from the zone center. PACS numbers: 71.15.m, 71.20.b, 71.70.Ej, Bismuth selenide has been widely studied for many years for its potential applications in optical recording systems [1], photoelectrochemical [2] and thermoelectric devices [3,4], and is nowadays commonly used in refrigeration and power generation. Recently, it has attracted increasing interest after its identification as a prototypical topological insulator (TI) [5,6]. Its surface electronic structure consists of a single Dirac cone around the surface Brillouin zone (SBZ) centreΓ, with the Dirac point (DP) placed closely above the bulk valence band states. In order to exploit the multitude of interesting phenomena associated with the topological surface states [7,8], it is necessary to access the topological transport regime, in which the chemical potential is near the DP and simultaneously in the absolute bulk band gap. Due to the close proximity of the DP and the bulk valence states at Γ, this is only possible if there are no other valence states in Bi 2 Se 3 with energies close to or higher than the DP. Therefore, it is crucial to establish if the bulk valence band maximum (VBM) in bismuth selenide is placed at Γ (and thus projected out toΓ) or at some other position within the Brillouin zone (BZ). As the bulk conduction band minimum (CBM) is undisputedly located at Γ [9,10], the question about the VBM location is identical to the question about the nature of the fundamental band gap in this TI, direct or indirect.The nature of the bulk band gap is thus of crucial importance for the possibility of exploiting the topological surface states in transport, but the position of the VBM in band structure calculations remains disputed. In a linearized muffin-tin orbital method (LMTO) calculation within the local density approximation (LDA), the VBM was found at the Γ point, implying that Bi 2 Se 3 is a direct-gap semiconductor [11]. Contrarily, by employing the full-potential linearized augmented-plane-wave method (FLAPW) within the generalized gradient approximation (GGA), the authors of Ref. 9 have found the VBM to be located on the Z − F line of the BZ, which is lying in the mirror plane. Similar results have been obtained in Ref. 12 with the plane-wave pseudopotential method (PWP) within the LDA. Various density functional theory (DFT) calculations of the surface band structure of Bi 2 Se 3 [5,7,13,14] also indicate that the VBM of bulk bismuth selenide is not located at the BZ center. The inclusion of many-body effects within the G...

We present self-energy calculations for Hg chalcogenides (HgX, X = S, Se, and Te) with inverted band structures using an explicit spin-dependent formulation of the GW approximation. Spin-orbit coupling is fully taken into account in calculating the single-particle Green function G and the screened interaction W . We have found, apart from an upward shift of the occupied conductionlike 6 state by about 0.7 eV, an enhancement of spin-orbit splitting by about 0.1 eV, in good agreement with experiment. This renormalization originates mainly from spin-orbit induced changes in G rather than W , which is affected only little by spin-orbit coupling.

Recently, Shih et al. [Phys. Rev. Lett. 105, 146401 (2010)] published a theoretical band gap for wurtzite ZnO, calculated with the non-self-consistent GW approximation, that agreed surprisingly well with experiment while deviating strongly from previous studies. They showed that a very large number of empty bands is necessary to converge the gap. We reexamine the GW calculation with the full-potential linearized augmented-plane-wave method and find that even with 3000 bands the band gap is not completely converged. A hyperbolical fit is used to extrapolate to infinite bands. Furthermore, we eliminate the linearization error for high-lying states with local orbitals. In fact, our calculated band gap is considerably larger than in previous studies, but somewhat (4)] is constructed from the Kohn-Sham Green function taken from a densityfunctional theory calculation with the local-density approximation (LDA) for the exchange-correlation energy functional. The quasiparticle energy E σ nq with band index n, Bloch vector q, and spin σ is then obtained from the nonlinear equation 5-8 invoking the one-shot LDA + GW approach showed that the band gap of wurtzite ZnO is underestimated with respect to the experimental value by more than 1 eV. They fall in the range 2.12-2.6 eV while the experimental gap amounts to 3.6 eV, 9 after correction for vibrational effects. This large underestimation is untypical for GW calculations of sp-bound systems.The Letter of Shih et al. addressed two issues: first, the erroneous hybridization effects between Zn 3d and O 2p states that results from the self-interaction error within the LDA, 10 and second, the band convergence in the correlation part of the self-energy. The first problem was tackled with the LDA + U approach, 11 in which an orbital-dependent potential corrects the position of the 3d bands and, thus, reduces hybridization effects with the O 2p states. However, the combination LDA + U and GW yields a band gap that is still well below the experimental value. Therefore, the authors investigated the second issue by carefully converging the correlation self-energy and the dielectric matrix with respect to the number of bands. They performed calculations with up to 3000 bands corresponding to a maximal band energy of 67 Ry as well as a cutoff for the dielectric matrix of up to 80 Ry and showed that the resulting GW band gaps, 3.4 eV for LDA + GW and 3.6 eV for LDA + U + GW , turned out to be in very good agreement with experiment. They also demonstrated that a too small energy cutoff for the dielectric matrix can lead to a false convergence behavior: the band gap seems to converge with many fewer bands, but toward a value that is too small.These new results for ZnO are in striking contrast to previous studies. If they are correct, they cast doubt on all GW calculations published so far, not only for ZnO but also for other materials, especially for systems with localized states. In fact, Shih et al. point out at the end of their paper that "many of the previous quasiparticle calculat...

This paper investigates the influence of the basis set on the GW self-energy correction in the fullpotential linearized augmented-plane-wave (LAPW) approach and similar linearized all-electron methods. A systematic improvement is achieved by including local orbitals that are defined as second and higher energy derivatives of solutions to the radial scalar-relativistic Dirac equation and thus constitute a natural extension of the LAPW basis set. Within this approach linearization errors can be eliminated, and the basis set becomes complete. While the exchange contribution to the self-energy is little affected by the increased basis-set flexibility, the correlation contribution benefits from the better description of the unoccupied states, as do the quasiparticle energies. The resulting band gaps remain relatively unaffected, however; for Si we find an increase of 0.03 eV.

We introduce an approach to derive realistic Coulomb interaction terms in free standing layered materials and vertical heterostructures from ab-initio modelling of the corresponding bulk materials. To this end, we establish a combination of calculations within the framework of the constrained random phase approximation, Wannier function representation of Coulomb matrix elements within some low energy Hilbert space and continuum medium electrostatics, which we call Wannier function continuum electrostatics (WFCE). For monolayer and bilayer graphene we reproduce full ab-initio calculations of the Coulomb matrix elements within an accuracy of 0.2 eV or better. We show that realistic Coulomb interactions in bilayer graphene can be manipulated on the eV scale by different dielectric and metallic environments. A comparison to electronic phase diagrams derived in [M. M. Scherer et al., Phys. Rev. B 85, 235408 (2012)] suggests that the electronic ground state of bilayer graphene is a layered antiferromagnet and remains surprisingly unaffected by these strong changes in the Coulomb interaction.