<i>Ab Initio</i>Calculation of Excitonic Effects in the Optical Spectra of Semiconductors

Albrecht, Stefan; Reining, Lucia; Sole, R. Del; Onida, Giovanni

doi:10.1103/physrevlett.80.4510

Cited by 865 publications

(717 citation statements)

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“…4. This scheme, using the approach of the effective twoparticle Hamiltonian, has again been applied to the calculation of the absorption spectrum of bulk silicon (Albrecht et al, 1998a), showing that the Bethe-Salpeter method used without any adjustable parameter can yield absorption spectra of continuum excitons in bulk semiconductors in quantitative agreement with experiment (see Fig. 5).…”

Section: The Effects Of the Electron-hole Interactionmentioning

confidence: 53%

“…5). 30 On the other hand, as pointed out above, the electronhole attraction can also lead to bound excitons in insu- 30 The present curve has been calculated by Olevano and Reining (2000) using an improved Brillouin-zone sampling with respect to the original publication of Albrecht et al (1998a). See also the discussions by Cardona et al (1999) and Albrecht et al (1999).…”

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%

“…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: 53%

Section: The Effects Of the Electron-hole Interactionmentioning

confidence: 99%

Section: Effective Hamiltonians and Effective Interactionsmentioning

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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“…In the standard scheme, the quasiparticle band structures are obtained using the Green's function G and screened Coulomb interaction W approximation, 7 while optical excitation energies are obtained by solving a Bethe-Salpeter equation (BSE) 8 with a statically screened electron-hole interaction. The GW-BSE approach 9,10 has been successfully applied to a number of different systems ranging from bulk semiconductors, 9 insulators and their surfaces, 11 two-dimensional systems such as graphene 12 and boron nitride layers, 13 metal-molecule interfaces, 6 isolated molecules, [14][15][16] and liquid water. 17 Nevertheless, applications of the approach to larger systems are limited by the extremely demanding computational requirements of both the GW and BSE calculations.…”

Section: Introductionmentioning

confidence: 99%

Optical properties of bulk semiconductors and graphene/boron nitride: The Bethe-Salpeter equation with derivative discontinuity-corrected density functional energies

2012

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We present an efficient implementation of the Bethe-Salpeter equation (BSE) for optical properties of materials in the projector augmented wave method GPAW. Single-particle energies and wave functions are obtained from the GLLBSC functional which explicitly includes the derivative discontinuity, is computationally inexpensive, and yields excellent fundamental gaps. Electron-hole interactions are included through the BSE using the statically screened interaction evaluated in the random phase approximation. For a representative set of semiconductors and insulators we find excellent agreement with experiments for the dielectric functions, onset of absorption, and lowest excitonic features. For the two-dimensional systems of graphene and hexagonal boron-nitride (h-BN) we find good agreement with previous many-body calculations. For the graphene/h-BN interface, we find that the fundamental and optical gaps of the h-BN layer are reduced by 2.0 eV and 0.7 eV, respectively, compared to freestanding h-BN. This reduction is due to image charge screening which shows up in the GLLBSC calculation as a reduction (vanishing) of the derivative discontinuity.

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First-principles calculations of electronic excitations in clusters

Reining

Pulci

Palummo

et al. 2000

Int. J. Quant. Chem.

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ABSTRACT:We discuss an approach to calculate electronic excitations in clusters, which starts from the determination of the ground state within density functional theory and the local density approximation, and subsequently yields electronic spectra from Green's function theory. These methods, which were originally developed and used in extended systems, are shown to work well also in clusters. We discuss the theory and the computational implementation, and illustrate the performance and the physical mechanisms of this approach for the example clusters Na 4

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Ab InitioCalculation of Excitonic Effects in the Optical Spectra of Semiconductors

Cited by 865 publications

References 36 publications

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

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

Optical properties of bulk semiconductors and graphene/boron nitride: The Bethe-Salpeter equation with derivative discontinuity-corrected density functional energies

First-principles calculations of electronic excitations in clusters

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