Polarization-resolved analysis of high-order harmonic generation in monolayer MoS 2

We employ a theoretical model based on the density-matrix equation in the velocity gauge to calculate high harmonic generation from monolayer MoS2. This approach incorporates the tight-binding model, enabling the full consideration of both crystal symmetry and multiple band effects. In additional to the usual odd harmonics, even harmonics are also presented in the case of observing two different polarization components, which are parallel and perpendicular to the polarization of linearly driving pulses. We detailedly analyze the crystal orientation dependence for the parallel and perpendicular components of both odd- and even-harmonics. It is found that they exhibits different modulation behavior with rotating the crystal orientation. The simulation results capture all important orientation-dependent features observed in the recent experiment, thus demonstrating that the Berry curvature of MoS(2)has been appropriately considered in our proposed model. In order to facilitate analysis of the underlying mechanism, we examine the channel current in terms of the contribution from different density-matrix elements, and identify their role in the orientation modulation of high harmonics. We further use simplified one-dimensional integral model to explain the appearance of perpendicular components of even harmonics. Our analysis shows that the multi-band coupling effect is the origin of the parallel even harmonics, while the broken inversion symmetry of phase difference of momentum matrix elements along two orthogonal directions determines the perpendicular even harmonic generation. Additionally, the relationship between the concept of Berry curvature and our theoretical framework is discussed. These demonstrations show that polarization-resolved high harmonics might provide an all-optical way for imaging material's Berry curvature.