We investigate the description of excitonic effects within time-dependent density-functional theory (TD-DFT). The exchange-correlation kernel f xc introduced in TDDFT allows a clear separation of quasiparticle and excitonic effects. Using a diagrammatic representation for f xc , we express its excitonic part f xc Ex in terms of the effective vertex function ⌳. The latter fulfills an integral equation that thereby establishes the exact correspondence between TDDFT and the standard many-body approach based on the Bethe-Salpeter equation (BSE).The diagrammatic structure of the kernel in the equation for ⌳ suggests the possibility of strong cancellation effects. Should the cancellation take place, already the first-order approximation to f xc Ex is sufficient. A potential advantage of TDDFT over the many-body BSE method is thus dependent on the efficiency of the above-quoted cancellation. We explicitly verify this for an analytically solvable two-dimensional two-band model. The calculations confirm that the low-order f xc Ex perfectly describes the bound exciton as well as the excitonic effects in the continuous spectrum in a wide range of the electron-hole coupling strength.
A diagrammatic expansion for the dynamic exchange-correlation kernel fxc of time dependent density functional theory is formulated. It is shown that fxc has no singularities at Kohn-Sham transition energies in every order of the perturbation theory. However, it may diverge with the system size in extended systems. This signifies that any approximate perturbative substitute for fxc requires a consistent perturbative treatment of the response function to avoid uncontrollable errors in the many-body corrections to excitations energies.
We extend standard k · p theory to take into account periodic perturbations which are rapidly oscillating with a wavelength of a few lattice constants. Our general formalism allows us to explicitly consider the Bragg reflections due to the perturbation-induced periodicity. As an example we calculate the effective masses in the lowest two conduction bands of spontaneously ordered GaInP2 as a function of the degree of ordering. Comparison of our results for the lowest conduction band to available experimental data and to first principle calculations shows good agreement. 71.20.Nr,71.15.Th,71.18.+y
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