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Register a new userA minimal model for excitons within time-dependent density-functional theory
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The accurate description of the optical spectra of insulators and semiconductors remains an important challenge for time-dependent density-functional theory (TDDFT). Evidence has been given in the literature that TDDFT can produce bound as well as continuum excitons for specific systems, but there are still many unresolved basic questions concerning the role of dynamical exchange and correlation (xc). In particular, the role of the long spatial range and the frequency dependence of the xc kernel $f_{rm xc}$ for excitonic binding are still not very well explored. We present a minimal model for excitons in TDDFT, consisting of two bands from a one-dimensional Kronig-Penney model and simple approximate xc kernels, which allows us to address these questions in a transparent manner. Depending on the system, it is found that adiabatic xc kernels can produce a single bound exciton, and sometimes two bound excitons, where the long spatial range of $f_{rm xc}$ is not a necessary condition. It is shown how the Wannier model, featuring an effective electron-hole interaction, emerges from TDDFT. The collective, many-body nature of excitons is explicitly demonstrated.
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Colloidal quantum dots (QDs) of group III-V are considered as promising candidates for next-generation environmentally friendly light emitting devices, yet there appears to be only limited understanding of the underlying electronic and excitonic properties. Using large-scale density functional theory with the hybrid B3LYP functional solving the single-particle states and time-dependent density functional theory accounting for the many-body excitonic effects, we have identified the structural, electronic and excitonic optical properties of InP, GaP and GaInP QDs containing up to a thousand atoms or more. The calculated optical gap of InP QD appears in excellent agreement with available experiments, and it scales nearly linearly with the inverse diameter. The radiative exciton decay lifetime is found to increase surprisingly linearly with increasing the dot size. For GaP QDs, we predict an unusual electronic state crossover at diameter around 1.5 nm whereby the nature of the lowest unoccupied molecular orbital (LUMO) state switches its symmetry from $Gamma_{5}$-like at larger diameter to $Gamma_{1}$-like at smaller diameter. After the crossover, the absorption intensity of the band-edge exciton states is significantly enhanced. Finally, we find that Vegards law holds very well for GaInP random alloyed quantum dots down to ultra-small sizes with less than a hundred atoms. The obtained energy gap bowing parameter of this common-cation compound in QD regime appears positive, size-dependent and much smaller than its bulk parentage. The volume deformation, dominating over the charge exchange and structure relaxation effects, is mainly responsible for the QD energy gap bowing. The present work provides a road map for a variety of electronic and optical properties of colloidal QDs in group III-V that can guide spectroscopic studies.
Linear-response time-dependent density-functional theory (TDDFT) can describe excitonic features in the optical spectra of insulators and semiconductors, using exchange-correlation (xc) kernels behaving as $-1/k^{2}$ to leading order. We show how excitons can be modeled in real-time TDDFT, using an xc vector potential constructed from approximate, long-range corrected xc kernels. We demonstrate for various materials that this real-time approach is consistent with frequency-dependent linear response, gives access to femtosecond exciton dynamics following short-pulse excitations, and can be extended with some caution into the nonlinear regime.
Time-dependent density-functional theory (TDDFT) is a computationally efficient first-principles approach for calculating optical spectra in insulators and semiconductors, including excitonic effects. We show how exciton wave functions can be obtained from TDDFT via the Kohn-Sham transition density matrix, both in the frequency-dependent linear-response regime and in real-time propagation. The method is illustrated using one-dimensional model solids. In particular, we show that our approach provides insight into the formation and dissociation of excitons in real time. This opens the door to time-resolved studies of exciton dynamics in materials by means of real-time TDDFT.
We introduce a new implementation of time-dependent density-functional theory which allows the emph{entire} spectrum of a molecule or extended system to be computed with a numerical effort comparable to that of a emph{single} standard ground-state calculation. This method is particularly well suited for large systems and/or large basis sets, such as plane waves or real-space grids. By using a super-operator formulation of linearized time-dependent density-functional theory, we first represent the dynamical polarizability of an interacting-electron system as an off-diagonal matrix element of the resolvent of the Liouvillian super-operator. One-electron operators and density matrices are treated using a representation borrowed from time-independent density-functional perturbation theory, which permits to avoid the calculation of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is evaluated through a newly developed algorithm based on the non-symmetric Lanczos method. Each step of the Lanczos recursion essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn-Sham Hamiltonian. Suitable extrapolation of the Lanczos coefficients allows for a dramatic reduction of the number of Lanczos steps necessary to obtain well converged spectra, bringing such number down to hundreds (or a few thousands, at worst) in typical plane-wave pseudopotential applications. The resulting numerical workload is only a few times larger than that needed by a ground-state Kohn-Sham calculation for a same system. Our method is demonstrated with the calculation of the spectra of benzene, C$_{60}$ fullerene, and of chlorofyll a.
I show that the so-called causality paradox of time-dependent density functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the paradox in real time, but also leads to a new expression for the causal exchange-correlation kernel in terms of Berry curvature. Furthermore, I show that all the results that were previously derived from symmetries of the action functional remain valid in the present formulation. Finally, I develop a model functional theory which explicitly demonstrates the workings of the new formulation.
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