Real-space, real-time method for the dielectric function

Bertsch, G. F.; Iwata, Junichi; Rubio, Ángel; Yabana, Kazuhiro

doi:10.1103/physrevb.62.7998

Cited by 369 publications

(276 citation statements)

References 21 publications

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“…10 using the formalism of Ref. 35 . The calculated real part of the static dielectric function is ǫ(0) = 12.6, close to the experimental value of 11.6.…”

Section: Discussionmentioning

confidence: 99%

“…The present formalism gives the same linear response as other approaches, so the weak field limit will be correct if the dielectric function is given correctly. In our previous work, we calculated the linear response by separating A into a part that arose from external sources and a part arises from the medium 35 . It is not necessary to make this separation in the present formalism.…”

Section: E Linear Responsementioning

confidence: 99%

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Time-dependent density functional theory for strong electromagnetic fields in crystalline solids

et al. 2012

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We apply the coupled dynamics of time-dependent density functional theory and Maxwell equations to the interaction of intense laser pulses with crystalline silicon. As a function of electromagnetic field intensity, we see several regions in the response. At the lowest intensities, the pulse is reflected and transmitted in accord with the dielectric response, and the characteristics of the energy deposition is consistent with two-photon absorption. The absorption process begins to deviate from that at laser intensities ∼ 10 13 W/cm 2 , where the energy deposited is of the order of 1 eV per atom. Changes in the reflectivity are seen as a function of intensity. When it passes a threshold of about 3 × 10 12 W/cm 2 , there is a small decrease. At higher intensities, above 2 × 10 13 W/cm 2 , the reflectivity increases strongly. This behavior can be understood qualitatively in a model treating the excited electron-hole pairs as a plasma.

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“…10 using the formalism of Ref. 35 . The calculated real part of the static dielectric function is ǫ(0) = 12.6, close to the experimental value of 11.6.…”

Section: Discussionmentioning

confidence: 99%

Section: E Linear Responsementioning

confidence: 99%

Time-dependent density functional theory for strong electromagnetic fields in crystalline solids

et al. 2012

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“…This method thus uses a direct solution of the timedependent single-electron Schrö dinger equation for the occupied states, (6.4) where H KS is the Kohn-Sham Hamiltonian and is the time-dependent density (r,t)ϭ ͚ iϭ1 occ i *(r,t) i (r,t). The solution of this equation relies on very simple sparsematrix-vector multiplications and on a numerical implementation of the unitary time evolution operator (Yabana and Bertsch, 1996Bertsch, Iwata, et al, 2000;. Hence, for example, in the case of the TDLDA approximation for a cluster, the solution of the matrix equation (5.15) with a given kernel f xc is equivalent to propagating the equation above for some femtoseconds (the number depending on the accuracy in energy for the spectrum; Yabana and Bertsch, 1996Bertsch, , 1999a) with a given (now timedependent) V xc .…”

Section: A the Equationsmentioning

confidence: 99%

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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“…[6][7][8][9][10][11][12][13][14] TDDFT provides access to excited state energies, geometries, and other properties of small molecules with a relatively moderate computational cost, similar to configuration interaction with single substitutions (CIS) in the linear response frequency-domain formulation 15 (O N 4 , where N is the number of electrons), or even better using a real-time implementation [16][17][18] (O N 2 ). In principle TDDFT is exact but in practice approximations have to be introduced.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent stochastic Bethe-Salpeter approach

2015

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A time-dependent formulation for electron-hole excitations in extended finite systems, based on the Bethe-Salpeter equation (BSE), is developed using a stochastic wave function approach. The time-dependent formulation builds on the connection between time-dependent Hartree-Fock (TDHF) theory and configuration-interaction with single substitution (CIS) method. This results in a timedependent Schrï¿oedinger-like equation for the quasiparticle orbital dynamics based on an effective Hamiltonian containing direct Hartree and screened exchange terms, where screening is described within the Random Phase Approximation (RPA). To solve for the optical absorption spectrum, we develop a stochastic formulation in which the quasiparticle orbitals are replaced by stochastic orbitals to evaluate the direct and exchange terms in the Hamiltonian as well as the RPA screening. This leads to an overall quadratic scaling, a significant improvement over the equivalent symplectic eigenvalue representation of the BSE. Application of the time-dependent stochastic BSE (TDsBSE) approach to silicon and CdSe nanocrystals up to size of ≈ 3000 electrons is presented and discussed.

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Real-space, real-time method for the dielectric function

Cited by 369 publications

References 21 publications

Time-dependent density functional theory for strong electromagnetic fields in crystalline solids

Time-dependent density functional theory for strong electromagnetic fields in crystalline solids

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

Time-dependent stochastic Bethe-Salpeter approach

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