Recently, a research team from the State Key Laboratory of Strong-Field Laser Physics, Shanghai Institute of Optical Precision and Mechanical Research (SIPMR), Chinese Academy of Sciences (CAS), has made progress in the frequency shift of even-order harmonics of monolayer MoS2 driven by strong-field laser. The results are published in Optics Express under the title "Frequency shift of even-order high harmonic generation in monolayer MoS2".
High-harmonic radiation in solid materials is an important spectroscopic technique for probing the fundamental properties of matter, and has been successfully used to reconstruct the energy band structure of crystals, probe the curvature of Berry, and detect topological phase transitions. In recent years, two-dimensional layered materials have received much attention, bringing new opportunities for further studies of high harmonic generation. Since the materials are only a single or a few atomic layers thick, their spatial scales are much smaller than the wavelength of the driving laser, bringing the advantage of effectively avoiding the effects of nonlinear transmission, thus making them ideal materials for studying laser field-driven ultrafast dynamics. Among them, monolayer molybdenum disulfide (MoS2) has attracted much attention from researchers due to its non-centrosymmetric structure and significant nonlinearity. The present research team [Opt. Express 29, 4830 (2021)] observed in the HHG spectra of MoS2 that the even harmonics exhibit anomalous enhancement and attributed it to the spectral interferences during the different half-weeks of the Berry liaison control . In addition, quantum trajectory analysis suggests that the leptonic dipole moment phase and the Berry liaison modulate the energy and momentum of the released photons, but so far no experimental observation has confirmed this.
The team used a laboratory-built mid-infrared laser light source to excite monolayer MoS2 to produce high-order harmonic spectra, and found that when driving the laser polarization along the armchair direction, the center frequency of the even-order harmonics is significantly shifted, and the frequency-shifted harmonic energy is close to that of the monolayer MoS2 bandgap energy. In addition, the frequency shift of the even harmonics of neighboring levels is found to be in the opposite direction, i.e., the 6th harmonic is red-shifted while the 8th harmonic is blue-shifted. Based on the semiconductor Bloch equation and electron-orbit saddle-point calculation, the research team successfully revealed the microphysical mechanism of the frequency shift generation, confirming that the frequency shift phenomenon of the even harmonics mainly comes from the interband polarization process. The theoretical analysis further shows that the phase of the jump dipole moment and the Bailey contact jointly modulate the moment and momentum of the electron-hole pair composite, leading to the change of the frequency of the released photons in the adjacent half-cycle, which in turn changes the center frequencies of the different harmonic levels, and ultimately induces the six red shifts and eight blue shifts of the MoS2 spectrum. This research work reveals that the phase of the jump dipole moment and Berry liaison have important roles in the strong-field optical response of non-centrosymmetric materials, which contributes to a fundamental understanding of ultrafast carrier dynamics in non-centrosymmetric materials.
Figure 1. Simulated high harmonic spectra reproducing experimental observations.
Fig. 2. (a) Frequency shift of different levels of interband spectra, (b) Dependence of harmonic frequency shift with crystal azimuth.
