High-harmonic generation from an atomically thin semiconductor

High-harmonic generation (HHG) in bulk solids permits the exploration of materials in a new regime of strong fields and attosecond timescales. The generation process has been discussed in the context of strongly driven electron dynamics in single-particle bands. Two-dimensional materials exhibit distinctive electronic properties compared to the bulk that could significantly modify the HHG process, including di erent symmetries, access to individual valleys and enhanced many-body interactions. Here we demonstrate non-perturbative HHG from a monolayer MoS2 crystal, with even and odd harmonics extending to the 13th order. The even orders are predominantly polarized perpendicular to the pump and are compatible with the anomalous transverse intraband current arising from the material’s Berry curvature, while the weak parallel component suggests the importance of interband transitions. The odd harmonics exhibit a significant enhancement in e ciency per layer compared to the bulk, which is attributed to correlation e ects. The combination of strong many-body Coulomb interactions and widely tunable electronicproperties in two-dimensionalmaterials o ersanew platform for attosecond physics. The recent observation of HHG in bulk solids provides a new approach to attosecond photonics and has opened up exciting opportunities for the study of strong-field and ultrafast electron dynamics in the condensed phase. HHG has been observed from various crystals, including ZnO, GaSe, SiO2 (ref. 3), and the rare-gas solids of Ar and Kr (ref. 6). Several theoretical models have been proposed for bulk HHG in terms of intraand interband electron dynamics; however, the underlying mechanism for HHG is still under debate, and a unified predictive theory that captures the diversity of solids remains elusive. Notably, it is not yet clear to what extent electron correlation affects the generation process. In the case of rare-gas solids, a second plateau is observed beyond the atomic limit. Although multiple plateaux can be explained within a single-particle picture, the position of the second plateau at twice the exciton energy suggests the importance of correlation effects in HHG processes in these solids. Such many-body effects are greatly enhanced in atomically thin layers, as exemplified by the observation of strongly bound excitons in monolayer transition metal dichalcogenides (TMDCs). In addition to strong electronic correlations, the valley-contrasting Berry curvature resulting from the broken inversion symmetry in the monolayers could give rise to the generation of even harmonics from intraband currents. Motivated by these distinctive properties of monolayer TMDCs, we have investigated the HHG from monolayer MoS2 crystals. Monolayer MoS2 is composed of two hexagonal layers of S atoms surrounding a central hexagonal layer of Mo atoms with trigonal prismatic coordination (inset of Fig. 1). Unlike the bulk crystal, with its bilayer unit cell, the monolayer breaks inversion symmetry. In our experiment, we probed HHG from a monolayer MoS2 crystal prepared on a fused silica substrate. We excited the sample at normal incidence with ∼160 fs mid-infrared pulses at a photon energy of 0.30 eV, well below the direct bandgap around 1.8 eV. Linearly polarized pump pulses with intensity up to 2.5 TWcm at a 1 kHz repetition rate were applied to the samplewithout noticeable damage. Figure 1 shows a representative high harmonic (HH) spectrum from amonolayer MoS2 crystal at a peak applied intensity of 2.2 TWcm. The field inside the monolayer is estimated at 0.33VÅ, taking into account the reflectivity of the substrate. At this field strength the laser imparts momentum to the electrons of magnitude comparable to the size of the Brillouin zone within a half laser cycle. Here the spectrum exhibits distinct peaks at integer multiples of the pump photon energy, corresponding to the 6th to 13th harmonic, above the direct bandgap. Both even and odd harmonics are present. The reported spectral range was defined by our detection scheme (see Methods for details). As we reduce the pump intensity, the strength of the harmonics decreases monotonically to the experimental noise level; we do not observe an abrupt cutoff for the generation of different harmonics. We measured the HH yield as a function of pump intensity I (Fig. 2). A power-law fit to the data yields an intensity dependence of I 3.3 for all orders (solid lines in Fig. 2). This result establishes the non-perturbative character of the generation process; in the perturbative limit, we would expect the hth harmonic yield to scale as the I h (dashed lines in Fig. 2). The role of crystal symmetry in the nonlinear optical response of monolayer MoS2 has been well established in the perturbative regime. Here we characterize the non-perturbative HHG from the monolayer in the context of crystal symmetry using a linearly polarized pump. The dependence on ellipticity is given in the Supplementary Information. We analyse the polarization components of the HH radiation, perpendicular and parallel to the linearly polarized fundamental field, as a function of crystal orientation (Fig. 3a,d). Figure 3b shows a false colour representation of the HH spectrum in the perpendicular configuration as a function of the angle θ between the pump polarization and the mirror plane of the crystal (Fig. 3a). The signal is dominated by the even orders (8th, 10th and 12th). The integrated harmonic yields of these orders are presented in Fig. 3c. As functions of the crystal orientation, the intensities of the even harmonics are strongly modulated with a common period of 60. The modulation of the various harmonics is in phase, and the modulation depths are near unity. When the mirror plane is parallel to the fundamental polarization (θ = 0, 60, 120, . . .), mirror symmetry requires the induced even harmonic current (and thus the corresponding harmonic radiation) perpendicular to the fundamental field to vanish. By symmetry, the perpendicular components of the odd