Optical Absorption of Insulators and the Electron-Hole Interaction: An<i>Ab Initio</i>Calculation

Benedict, Lorin X.; Shirley, Eric L.; Bohn, Robert B.

doi:10.1103/physrevlett.80.4514

Cited by 489 publications

(364 citation statements)

References 16 publications

(12 reference statements)

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“…lators, where the interaction is only weakly screened. The resulting spectra can also be well described by the ab initio Bethe-Salpeter approach, as has been illustrated by the work of Benedict et al (1998a). These authors use a recursive method (Haydock, 1980) to invert the Bethe-Salpeter equation (4.9), which has the advantage that one can make use of the ␦ functions in the W contribution to the kernel in order to make calculations less cumbersome.…”

Section: The Effects Of the Electron-hole Interactionmentioning

confidence: 91%

“…Moreover, they have studied the wide-gap semiconductor GaN (in its wurtzite and zincblende structures), and the insulating CaF 2 crystal (Benedict and Shirley, 1999). In all cases, the inclusion of excitonic effects turned out to be crucial for a quantitative agreement between theory and experiment.…”

Section: The Effects Of the Electron-hole Interactionmentioning

confidence: 99%

“…The Na 4 cluster was the first realistic system to be treated in the ab initio scheme starting from DFT and going through GW (Onida et al, 1995), with a particularly strong effect of the electron-hole interaction due to the finite size of the cluster: the first absorption peak was moved back by 1.5 eV from its GW position, with a result close to the experimental one. An increasing number of such ab initio calculations of excitonic effects in finite and extended systems (see, for example, Albrecht et al, 1997Albrecht et al, , 1998aAlbrecht et al, , 1998bBenedict et al, 1998aBenedict et al, , 1998bLouie, 1998a, 1998b) have appeared since then, generally showing a big improvement over the results of RPA and GW-RPA calculations.…”

Section: Effective Hamiltonians and Effective Interactionsmentioning

confidence: 99%

“…Other scalings, namely, M 8 or M 10 , are obtained by also including triply or quadruply excited determinants. The approaches which will be discussed in this review can exhibit a much better scaling, according to the system and to the numerical implementation (Benedict et al, 1998a;Hahn et al, 2002;Vasiliev et al, 2002).…”

Section: Overviewmentioning

confidence: 99%

“…The ab initio approaches used today for solution of the Bethe-Salpeter equation (Albrecht et al, 1998a(Albrecht et al, , 1998bBenedict et al, 1998a;Rohlfing and Louie, 1998b) mostly follow the scheme introduced by Onida et al (1995) for the spectrum of the cluster Na 4 and that of Albrecht et al (1997) for the optical gap of bulk Li 2 O. This procedure consists of (i) a ground-state DFT calculation; (ii) a GW calculation to correct the eigenvalues; and (iii) solution of the Bethe-Salpeter equation using GW eigenvalues, Kohn-Sham orbitals, and static RPA screening for the electron-hole interaction.…”

Section: The Effects Of the Electron-hole Interactionmentioning

confidence: 99%

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Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

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Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy ⌺ and the electron-hole interaction. A good approximation for ⌺ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of ⌺. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress. CONTENTS

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Section: The Effects Of the Electron-hole Interactionmentioning

confidence: 91%

Section: The Effects Of the Electron-hole Interactionmentioning

confidence: 99%

Section: Effective Hamiltonians and Effective Interactionsmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

Section: The Effects Of the Electron-hole Interactionmentioning

confidence: 99%

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Electronic excitations: density-functional versus many-body Green’s-function approaches

2002

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Present Status of the Theory of Surface Optical Properties

Sole

1998

phys. stat. sol. (a)

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Optical Reflectivity of the Si(111)-(2×1) Surface — The Role of the Electron–Hole Interaction

Rohlfing¹,

Louie

1999

phys. stat. sol. (a)

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We calculate the optical reflectivity of the Si(111)‐(2×1) surface from first principles. To this end, we first calculate the quasiparticle band structure of the surface within the GW approximation for the electronic self energy. The band structure exhibits two surface bands inside the fundamental bulk band gap. Thereafter the electron–hole interaction is computed for transitions between the relevant bands, the Bethe‐Salpeter equation for coupled electron–hole excitations is solved and the optical response is evaluated. In the energy range below the fundamental bulk band gap, the reflectivity spectrum is dominated by a surface exciton at 0.43 eV with an excitonic binding energy of 0.26 eV. Our calculated spectrum is in very good agreement with experimental data from differential reflectivity spectroscopy.

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Optical Absorption of Insulators and the Electron-Hole Interaction: AnAb InitioCalculation

Cited by 489 publications

References 16 publications

Electronic excitations: density-functional versus many-body Green’s-function approaches

Electronic excitations: density-functional versus many-body Green’s-function approaches

Present Status of the Theory of Surface Optical Properties

Optical Reflectivity of the Si(111)-(2×1) Surface — The Role of the Electron–Hole Interaction

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