Time-dependent density-functional theory for ultrafast interband excitations

Abstract

We formulate a time-dependent density-functional theory ͑TDDFT͒ in terms of the density matrix to study ultrafast phenomena in semiconductor structures. A system of equations for the density-matrix components, which is equivalent to the time-dependent Kohn-Sham equation, is derived. From this, we obtain a TDDFT version of the semiconductor Bloch equations, where the electronic many-body effects are taken into account, in principle, exactly. As an example, we study the optical response of a three-dimensional two-band insulator to an external short-time pulsed laser field. We show that the optical absorption spectrum acquires excitonic features when the exchange-correlation potential contains a 1 / q 2 Coulomb singularity. A qualitative comparison of the TDDFT optical absorption spectra with the corresponding results obtained within the Hartree-Fock approximation is made.

Estimating Excitonic Effects in the Absorption Spectra of Solids: Problems and Insight from a Guided Iteration Scheme

“…However, it fails to reproduce bound excitons, unless α is set ad hoc to a much higher value than in [25]. In this case, a transition may appear within the quasiparticle gap [29][30][31], but with too high oscillator strength [29].…”

“…However, it fails to reproduce bound excitons, unless α is set ad hoc to a much higher value than in [25]. In this case, a transition may appear within the quasiparticle gap [29][30][31], but with too high oscillator strength [29].Alternatively, the so-called bootstrap (BO) kernel [32] also has the correct 1/q 2 behavior; the prefactor is determined self-consistently, and it goes beyond the scalar version. Promising results have been published [32,33] for continuum and bound excitons, and the exciton binding energies of a range of small-and large-gap semiconductors have been calculated [34,35].…”

Time-Dependent Density-Functional Theory and Excitons in Bulk and Two-Dimensional Semiconductors

“…, see, e.g., [4]). In the linear response theory approximation in the case of weak pulses one can put in these equations n ck (t) = 1, n vk (t) = 0.…”

“…Indeed, such a kernel was successfully applied to describe excitonic effects in bulk and 2D materials [4,5,[15][16][17][18][19]. Unfortunately, the corresponding results strongly depend on the value of the parameter α and the relation α ∼ 1/ε may not necessarily hold for all materials.…”

“…Unfortunately, in the case of solids, standard TDDFT XC potentials, like adiabatic local density approximation (LDA) and generalized gradient approximation (GGA), do not give excitonic peaks in the absorption spectrum, or give such peaks with extremely small binding energies (see, e.g., [3][4][5]). Therefore, until very recent times the studies of excitons in semiconductors were almost universally based on a combined ab initio + many body approach, in which the GW calculations of the single-particle electronic structure were succeeded by calculations of the two-particle spectrum (that may include excitonic peaks) by solving the Bethe-Salpeter equation (BSE).…”