Unexpected increase of intensity-dependent excitonic second- and third-harmonic generation induced by static electric fields

TL;DR

The paper addresses how a homogeneous in-plane static electric field $E_{dc}$ modifies resonantly excited excitonic SHG and THG in a 2D MoS$_2$ homobilayer. It employs microscopic simulations by solving the semiconductor Bloch equations with many-body Coulomb interactions in time-dependent Hartree–Fock for a four-band intralayer exciton model, using a quasi-2D Coulomb potential and an ab initio-informed band structure. The key finding is that, under resonant excitation of the 1s K-exciton, SHG and THG exhibit complex, field-dependent behavior: SHG can increase superlinearly with $E_{dc}$ and THG can be enhanced with $E_{dc}$ at strong optical driving, due to a synergy of static and dynamic Stark shifts, exciton ionization, Wannier–Stark localization, off-resonant Rabi oscillations, and modified interference from intraband acceleration. The results reveal new routes to control strong-field exciton dynamics in 2D materials and suggest extensions to terahertz-driven schemes for enhanced nonlinear optical responses.

Abstract

We compute and analyze the dependence of excitonic second- and third-harmonic generation (SHG/THG) as a function of the optical excitation intensity in the presence of static electric fields by solving the semiconductor Bloch equations. Our simulations are performed for excitation of the strongly bound intralayer exciton of an inversion-symmetric homobilayer of MoS2 with in-plane electric fields. We demonstrate that for resonant excitation at the 1s K-exciton the SHG and the THG show complex dependencies on both the strength of the static field and the peak amplitude of the optical pulse. For sufficiently intense optical excitation, the THG increases and the SHG increases superlinearly with the amplitude of the static field as long as exciton ionization is not yet dominating. Microscopic simulations demonstrate that these dependencies arise from an interplay between several effects including static and transient Stark shifts, exciton ionization, Wannier-Stark localization, off-resonant Rabi oscillations, and a modified interference between optical nonlinearities induced by the intraband acceleration. Our findings offer several new possibilities for controlling the strong-field dynamics of systems with strongly bound excitons.

Figures (7)

• Figure 1: Calculated linear absorption spectra for a freestanding 2H homobilayer $MoS_2$. With increasing static field amplitude $E_{dc}$ all excitons Stark-shift to lower energies. Simultaneously, the peak absorption is reduced and the absorption lines broaden due to exciton ionization. For $E_{dc}\ge0.8~MV/cm$ weak periodic oscillations appear which originate from WS localization. The curves are shifted vertically for clarity.
• Figure 2: Ratio between $|P_{2\omega_0}|$ and ${E_{opt}}^2$ with $|P_{2\omega_0}|=\int_{1.7\omega_0}^{2.3\omega_0}|P(\omega)|d\omega$ for various optical and static field amplitudes. The excitation frequency is $\hbar\omega_0=1.936~eV/2$. Inset: Normalized $|P_{2\omega_0}|/E_{dc}$ as a function of the static field amplitude for $E_{opt}=0.5~MV/cm$ (solid dotted line) and $E_{opt}=5.5~MV/cm$ (dashed dotted line). The symbols represent the calculated values and the lines are guides for the eye.
• Figure 3: Ratio between $|P_{3\omega_0}|$ and ${E_{opt}}^3$ with $|P_{3\omega_0}|=\int_{2.7\omega_0}^{3.3\omega_0}|P(\omega)|d\omega$ for various optical and static field amplitudes. The excitation frequency is $\hbar\omega_0=1.936~eV/3$. Inset: Normalized $|P_{3\omega_0}|$ as a function of static field amplitude for $E_{opt}=0.5~MV/cm$ (solid dotted line) and $E_{opt}=5.5~MV/cm$ (dashed dotted line). The symbols represent the calculated values and the lines are guides for the eye.
• Figure 4: Linear absorption spectra in the presence of a cw optical field with (a) $\hbar\omega_{cw}=1.936~eV/2$ and (b) $\hbar\omega_{cw}=1.936~eV/3$. (c) and (d) show the energetic shift of the main exciton resonance compared to the field-free position of the 1s exciton due to both static and cw optical fields for the cw fields used in (a) and (b), respectively. The oscillatory results for $E_{dc}\ge 0.7~MV/cm$ arise from WS localization. In this regime the largest excitonic WS peaks shows an oscillatory dependence on $E_{dc}$.
• Figure 5: $\hbar \omega_{shift}(t)$ of the SHG frequency for (a) varying the optical field amplitude with $E_{dc}=0.1~MV/cm$, (b) varying the static field amplitude with $E_{opt}=0.5~MV/cm$, and (c) the same as in (b) but for $E_{opt}=8.0~MV/cm$. The excitation parameters are the same as those used in Fig. \ref{['fig2']}. The duration of an optical cycle is $4.27~fs$.