Compensation of Dynamical Quasiparticle and Vertex Corrections in Optical Spectra

Abstract

The inclusion of dynamical quasiparticle effects lifts the underestimation of band gaps in semiconductors and insulators derived within density-functional theory. Simultaneously, they give rise to a remarkable reduction of the strengths of the quasiparticle peaks that is not observed in optical spectra. We show that dynamical contributions to the vertex corrections widely compensate the peak renormalization due to the dynamics in the quasiparticle formation. The slight reduction of the absorption spectrum yields an improvement of the computed f-sum rule. [S0031-9007(97)02512-X] PACS numbers: 71.35.Cc, 71.45.Gm, 78.20.Bh The recent major advances in the quantitative computation of ground-state properties of solids are essentially related to the development of density-functional theory (DFT) in local-density approximation (LDA) [1]. However, spectroscopic properties, as optical spectra, are not accessible in this theory, since its single-particle eigenvalues or differences of them cannot be directly identifed with electronic excitation energies. For instance, energy gaps of semiconductors and insulators are remarkably underestimated within DFT-LDA [2]. Instead, quasiparticle (QP) energies have to be computed. The basic approach to quasiparticles is Hedin's GW approximation [3], in which the spatially nonlocal and energy-dependent exchange-correlation (XC) self-energy S is approximated by a convolution of single-particle Green function G and dynamically screened Coulomb interaction W. Vertex corrections are neglected. Full numerical calculations of the single-particle excitations can now be performed on real crystals starting from the DFT-LDA results [4,5]. The effect of the XC self-energy is not restricted to shift the single-particle energy from the DFT-LDA value for a certain band n and Bloch wave vector k to the QP position´n͑k͒. Rather, the energy dependence of the self-energy, b n ͑k͒ 2≠S͑ ͑ ͑nk,´n͑k͒͒ ͒ ͒͞≠´n͑k͒, gives rise to a considerable reduction of the spectral strength ͓1 2 b n ͑k͔͒ of the main QP peak by about 25% and to the simultaneous appearance of satellite structures in the single-QP spectral function. The strongest satellites appear around the plasmon energy of the system and its replicas [6]. Applying the QP results to optical spectra, the question arises if the oscillator strength of a certain direct electronic transition from a valence band y to a conduction band c at the wave vector k in the Brillouin zone (BZ) has to be reduced by a factor ͓1 2 b cy ͑k͔͒ with b cy ͑k͒ b c ͑k͒ 1 b y ͑k͒, i.e., by about 50%. A recent calculation by Del Sole and Girlanda [7] has shown that this is indeed the result, if the polarizability is calculated according to the strict GW-RPA method, namely, neglecting vertex corrections but including dynamicalself-energy effects. Since dynamical effects worsen the agreement between theory and experiment, they are usually neglected in calculating the dielectric function of a system within the independent QP approximation (i.e., neglecting excitonic effects) [8-10], al...

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