Time-dependent density-functional theory for ultrafast interband excitations (original) (raw)
Related papers
Analytical approach to semiconductor Bloch equations
EPL (Europhysics Letters), 2009
Although semiconductor Bloch equations have been widely used for decades to address ultrafast optical phenomena in semiconductors, they have a few important drawbacks: (i) Coulomb terms between free electron-hole pairs require Hartree-Fock treatment which, in its usual form, preserves excitonic poles but loses biexcitonic resonances. (ii) Solving the resulting coupled differential equations imposes heavy numerics which completely hide the physics. This can be completely avoided if, instead of free electron-hole pairs, we use correlated pairs, i.e., excitons. Their interactions are easy to handle through the recently constructed composite-exciton manybody theory, which allows us to analytically obtain the time evolution of the polarization induced by a laser pulse. This polarization comes from Coulomb interactions between virtual excitons, but also from Coulomb-free fermion exchanges, which are dominant at large detuning.
Excitonic effects in solids described by time-dependent density-functional theory
Physical review letters, 2002
Starting from the many-body Bethe-Salpeter equation we derive an exchange-correlation kernel f(xc) that reproduces excitonic effects in bulk materials within time-dependent density functional theory. The resulting f(xc) accounts for both self-energy corrections and the electron-hole interaction. It is static, nonlocal, and has a long-range Coulomb tail. Taking the example of bulk silicon, we show that the -alpha/q(2) divergency is crucial and can, in the case of continuum excitons, even be sufficient for reproducing the excitonic effects and yielding excellent agreement between the calculated and the experimental absorption spectrum.
Time-Dependent Density-Functional Theory and Excitons in Bulk and Two-Dimensional Semiconductors
Comput., 2017
In this work, we summarize the recent progress made in constructing time-dependent density-functional theory (TDDFT) exchange-correlation (XC) kernels capable to describe excitonic effects in semiconductors and apply these kernels in two important cases: a “classic” bulk semiconductor, GaAs, with weakly-bound excitons and a novel two-dimensional material, MoS2, with very strongly-bound excitonic states. Namely, after a brief review of the standard many-body semiconductor Bloch and Bethe-Salpether equation (SBE and BSE) and a combined TDDFT+BSE approaches, we proceed with details of the proposed pure TDDFT XC kernels for excitons. We analyze the reasons for successes and failures of these kernels in describing the excitons in bulk GaAs and monolayer MoS2, and conclude with a discussion of possible alternative kernels capable of accurately describing the bound electron-hole states in both bulk and two-dimensional materials.
Journal of Physics: Conference Series, 2012
We describe a unified formulation of time-dependent Hartree-Fock (TD-HF) and time-dependent density-functional theory (TD-DFT) for the accurate and efficient calculation of the optical response of infinite (periodic) systems. The method is formulated within the linear-response approximation, but it can easily be extended to include higher-order response contributions, and, in TD-DFT, it can treat with comparable computational efficiency purely local, semi-local or fully non-local approximations for the ground-state exchange-correlation (XC) functional and for the response TD-DFT XC kernel in the adiabatic approximation. At variance with existing methods for computing excitation energies based on the diagonalisation of suitable coupling matrices, or on the inversion of a dielectric matrix, our approach exploits an iterative procedure similar to a standard self-consistent field calculation. This results in a particularly efficient treatment of the coupling of excitations at different k points in the Brillouin zone. As a consequence, our method has the potential to describe completely from first principles the optically induced formation of bound particle-hole pairs in wide classes of materials. This point is illustrated by computing the optical gaps of a series of representative bulk semiconductors, (non-spin polarised) oxides and ionic insulators.
Physical Review B, 2014
We analyze possible nonlinear exciton-exciton correlation effects in the optical response of semiconductors by using a time-dependent density-functional theory (TDDFT) approach. For this purpose, we derive the nonlinear (third-order) TDDFT equation for the excitonic polarization. In this equation, the nonlinear time-dependent effects are described by the time-dependent (non-adiabatic) part of the effective exciton-exciton interaction, which depends on the exchange-correlation (XC) kernel. We apply the approach to study the nonlinear optical response of a GaAs quantum well. In particular, we calculate the 2D Fourier spectra of the system and compare it with experimental data. We find that the memory effects play a crucial role in this response, and in particular that it is necessary to use a non-adiabatic XC kernel to describe excitonic bound states-biexcitons, which are formed due to the retarded TDDFT exciton-exciton interaction.
Time-dependent density-matrix functional theory for biexcitonic phenomena
2010
We formulate a time-dependent density-matrix functional theory (TDDMFT) approach for higherorder correlation effects like biexcitons in optical processes in solids based on the reduced twoparticle density-matrix formalism within the normal orbital representation. A TDDMFT version of the Schrödinger equation for biexcitons in terms of one-and two-body reduced density matrices is derived, which leads to finite biexcitonic binding energies already with an adiabatic approximation. Biexcitonic binding energies for several bulk semiconductors are calculated using a contact biexciton model.
Time-dependent density functional theory of high excitations: to infinity, and beyond
Physical Chemistry Chemical Physics, 2009
We review the theoretical background for obtaining both quantum defects and scattering phase shifts from time-dependent density functional theory. The quantum defect on the negative energy side of the spectrum and the phase shift on the positive energy side merge continuously at E = 0, allowing both to be found by the same method. We illustrate with simple one-dimensional examples: the spherical well and the delta well potential. As an example of a real system, we study in detail elastic electron scattering from the He + ion. We show how the results are influenced by different approximations to the unknown components in (time-dependent) density functional theory: the ground state exchange-correlation potential and time-dependent kernel. We also revisit our previously obtained results for e-H scattering. Our results are remarkably accurate in many cases, but fail qualitatively in others. Contents
Optical Properties of Nanostructures from Time-Dependent Density Functional Theory
Journal of Computational and Theoretical Nanoscience, 2004
We review the time-dependent density functional theory (TDDFT) and its use to investigate excited states of nanostructures. These excited states are routinely probed using electromagnetic fields. In this case, two different regimes are usually distinguished: (i) If the electromagnetic field is "weak"as in optical absorption of light-it is sufficient to treat the field within linear response theory; (ii) Otherwise, nonlinear effects are important, and one has to resort to the full solution of the timedependent Kohn-Sham equations. This latter regime is of paramount relevance in the emerging field of research with intense and ultrashort laser pulses. This review is divided into two parts: First we give a brief overview of the theoretical foundations of the theory, both in the linear and non-linear regimes, with special emphasis on the problem of the choice of the exchange-correlation functional. Then we present a sample of applications of TDDFT to systems ranging from atoms to clusters and to large biomolecules. Although most of these applications are in the linear regime, we show a few examples of non-linear phenomena, such as the photo-induced dissociation of molecules. Many of these applications have been performed with the recently developed code octopus (http://www.tddft.org/programs/octopus).