Real-time exciton dynamics in two-dimensional materials under ultrashort laser pulses

Abstract

The optical response of two-dimensional materials is often significantly impacted by excitonic effects due to the reduced screening of attractive Coulomb interactions in low-dimensional systems. Accurate modeling of exciton formation and real-time dynamics is essential to understanding their ultrafast optical properties. In this study, we theoretically investigate the exciton dynamics in a two-dimensional hexagonal boron nitride (h-BN) and a germanium sulfide (GeS) monolayers exposed to an ultrashort laser pulse. We analyze the system's response to the external field in one- and two-photon excitation regimes. For our calculations, we combine a state-of-the-art ab initio approach to study exciton dynamics with a highly precise numerical scheme. We incorporate electron-hole interactions through a non-local self-energy operator derived from the many-body perturbation theory (MBPT) within the time-dependent adiabatic $GW$ (TD-a$GW$) approximation. We implement this approach using the full-electron LAPW+lo method in the all-electron exciting package. Our results elucidate the role of many-body effects in shaping ultrafast excitonic processes in two-dimensional materials, contributing to the fundamental understanding necessary for optoelectronic and photonic applications.

Figures (7)

• Figure 1: Scheme of the considered orientation of the honeycomb h-BN structure in real space. Unit cells are shown with solid black lines. Black circles represent B atoms, and gray circles represent N atoms.
• Figure 2: (a) Band structure and partial density of states of the h-BN monolayer in the ground state obtained within the DFT framework. The conduction band is shifted 2.62 eV upwards via the scissor operator \ref{['eq:scissor']} to mimic the $GW$ quasiparticle gap. (b) Imaginary part of the dielectric function Im $\varepsilon$ of an h-BN monolayer calculated with time-domain response to the delta-shaped pulse. The IPA curve was obtained within the independent particle approximation (Eq. \ref{['eq:hamIPA']}), while the TD-a$GW$ curve is obtained with the full Hamiltonian \ref{['eq:hamFull']}. The dashed BSE curve is obtained with the BSE. Lorentzian broadening of 0.1 eV is included in the postprocessing-stage Fourier transform.
• Figure 3: Scheme of the considered orientation of the GeS monolayer in real space. Unit cells are shown with solid black lines. Black circles represent Ge atoms, and gray circles represent S atoms. Direction $x$ is the "armchair" direction, and $y$ is the "zigzag" one.
• Figure 4: (a) Band structure and partial density of states of the GeS in the ground state obtained within the DFT framework. The conduction band is shifted by 1.07 eV upwards via the scissor operator \ref{['eq:scissor']} to mimic the $GW$ quasiparticle band gap. (b) Imaginary part of the dielectric function Im $\varepsilon_{xx}$ of a GeS monolayer calculated with time-domain response to the delta-shaped pulse. The IPA curve was obtained within the independent particle approximation (Eq. \ref{['eq:hamIPA']}), while the TD-a$GW$ curve is obtained with the full Hamiltonian \ref{['eq:hamFull']}. Lorentzian broadening of 0.1 eV is included in the postprocessing-stage Fourier transform. Direction $x$ is the "armchair" direction of a GeS monolayer.
• Figure 5: (a) Time-dependent macroscopic residual polarization $P_y$ in an h-BN monolayer after excitation by a linearly-polarized, $\sin^2$-shaped pulse with a central photon energy of 6.12 eV (top panel), 3.06 eV (bottom panel), and a duration of 830 a.u. ($\approx$ 21 fs). On the top panel, vertical dashed lines mark the moments in time, when the time-dependent excitonic state is almost $2s$-like (left line), and $2p$-like (right line). (b) Top row: conduction band occupations in an h-BN monolayer after excitation by the short linearly-polarized pulse with a central photon energy 6.12 eV at $t \approx$ 25 fs (left) and $t \approx$ 32.5 fs (right) in reciprocal space. The selected time points correspond to the vertical lines in Fig. \ref{['fig:beats']}. Bottom row: change in the occupations of unperturbed states along the standard $\bm{k}$-path at the same times. Red and blue colors indicate the positive and negative charge differences, respectively, while point size represents the magnitude of the change.