Role Of Dynamical Symmetry And Valley Selection In High Harmonic Generation In Solids

In recent years,due to the rapid development of ultra-intense ultrashort-laser technology,the ultrafast process in solids,such as high harmonic generation(HHG)has become one of the most attractive fields and frontier of ultrafast science.Crystals have short interatomic spacing and high density.In addition to translational symmetry crystals may possess some rotational and reflection symmetries and inversion symmetry and so on.The tailored laser fields can possess desired field symmetries,such as discrete rotational symmetry.The associated symmetry of the laser-target system plays a key role in the process of HHG in solids.In this thesis,we theoretically studied the role of dynamical symmetry in one-dimensional Zn O crystal with inversion symmetry and monolayer molybdenum disulfide(Mo S2)crystal with broken inversion symmetry by combining the semi-conductor Bloch equation with the strong-field approximation(SFA)for solids and classical model for HHG in solids.The main achievements are as follows:1.One-dimensional Zn O crystal(along the?-M direction)with inversion symmetry is investigated.Based on the analysis of the interference between the harmonics,for harmonics generated by a set of symmetrical crystal-momentum channels,the results show that constructive interferences always occur between odd order harmonics and destructive interferences always occur between even-order harmonics,so the final form of the odd-order harmonics-dominated harmonic spectrum.Based on the SFA description of the interband current in solid,we analytically prove that the constructive interferences between odd-order harmonics and the destructive interferences between even-order harmonics are determined by the inversion symmetry of the band dispersion along the?-M direction and the time translation symmetry of the laser field.2.Based on the quasi-classical model in k space,we propose and numerically demonstrate a method independent on the birth time and recollision time to select the short and long trajectories for HHG in solids.Our method works well for both quantum trajectories conformed with the quasiclassical trajectories(QTQ)and quantum trajectories conformed with the recollision trajectories(QTR).It is found that the short(long)QTR are formed by the short(long)QTQ of all the momentum channels in the entire first Brillouin zone(BZ).This means that,from the physical sense,recollision trajectories is not a subset of quasiclassical trajectories,one can consider the recollision trajectories as the collective effects of the quasiclassical trajectories,QTR are formed by the interferences between the harmonics contributed by all the momentum channels in the entire first BZ.Our results clarify the relationship between the classical trajectories predicted by the quasiclassical model in _k space and the classical trajectories predicted by the real-space recollision model.3.For the system of the tailored lasers with discrete rotational symmetry and monolayer Mo S2 crystal with broken inversion symmetry,it is found that circularly polarized high harmonics can be efficiently generated in monolayer Mo S2 driven by counterrotating bicircular(CRB)fields.Based on the valley resolved and polarization resolved harmonic spectra,it is found that the valley-selective circular dichroism(VSCD)of monolayer Mo S2 lead to a distinctive valley selection of harmonic orders,while the valley selection caused by the trefoil orientation relative to the lattice is also observed.4.Based on dynamical symmetry analysis,the“lowest common multiple(LCM)rule”is proposed to determine the allowed number of folds in the pattern of direction-dependent yields for above-gap,interband harmonics.It is found that,for a system consisting of a laser with L-fold rotational symmetry and a target with in-plane M-fold rotational symmetry,the allowed number of folds in the pattern of yields of harmonics equal to the LCM of L and M.The LCM rules can be qualitatively understood by a real-space picture for HHG in solids.Therefore,it is concluded that the rotational symmetry of the crystals can be exactly decoded by the combination of a linearly polarized excitation scheme and CRB excitation scheme via the LCM rule.5.We also illustrate the fingerprints of VSCD leaving in harmonic spectra.Different from that of the gas medium where the ellipticity of every harmonic can be controlled by adjusting the ellipticity of the driving lasers,the ellipticities of the(3_n+1)th and(3_n+2)thharmonics dominated by the interband mechanisms in monolayer Mo S₂ are insensitive to the driver's ellipticity.Based on a single-band model,we exclude the effects of berry curvature and band group velocity,and confirm that this is caused by the VSCD of monolayer MoS2.