Real-Time Exciton Dynamics with Time-Dependent Density-Functional Theory

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.

Figure 1

Optical spectra $\mathrm{Im}(ϵ)$ of Si, obtained by LR- and RT-TDDFT, compared with BSE and experiment [66]. The calculated spectra are scissor shifted for the onset to line up with experiment (see SM for details [45]).

Figure 2

Response of Si to 10 fs laser pulses (frequency 1.6 eV, polarized along $z$) with peak intensities ${10}^7\mathrm{W}/{\mathrm{cm}}^2$ (top) and ${10}^{11}\mathrm{W}/{\mathrm{cm}}^2$ (bottom), comparing ALDA and ${\mathrm{LRC}}_{+}$ within RT-TDDFT. (a) Induced current density $j_z(t)$. (b) Dipole power spectrum $|P(\omega ){|}^2$.

Figure 3

Strongly bound excitons in an ${\mathrm{H}}_2$ chain (left) and LiF (right). (a) $\mathrm{Im}(ϵ)$ from BSE and TDDFT; (b) macroscopic current density from RT ALDA and LRC with $\alpha =8$ and 18; (c) $\mathrm{Im}(ϵ)$ from ${\mathrm{LRC}}_{+}$ in LR and RT, with $\alpha$ and $\beta$ as indicated, versus experiment [68]; (d) macroscopic current density from the same three $\mathrm{RT}\text{−}{\mathrm{LRC}}_{+}$ as in (c).

Figure 4

Optical spectra of ${\mathrm{CsGeCl}}_3$ obtained by BSE and RT-TDDFT using APBE and ${\mathrm{LRC}}_{+}^{*}$.