Inter-half-cycle spectral interference in high-order harmonic generation from monolayer MoS₂

Abstract

The enhancement of even-order harmonics near the cut-off of high-order harmonic spectra from monolayer MoS2 has been experimentally observed recently by several groups. Here we demonstrate that this enhancement can be interpreted as a result of spectral interference between half-cycles with opposite polarity by adopting a fully quantum mechanical calculation. We found that, due to the energy modulation induced by Berry connections, only half-cycles with the same polarity can generate high-order harmonics near the cut-off frequency, thus the lack of destructive interference leads to the enhanced intensity of the corresponding even-order harmonics. The explanation is supported by the frequency shift of the measured harmonic peaks. Our finding revealed the role of inter-half-cycle interference in high-harmonic generation (HHG) from non-centrosymmetric materials.

Signatures of multi-band effects in high-harmonic generation in monolayer MoS$_2$

“…Note that a similar 30 • -periodicity was recently experimentally observed in GaSe [46] and the topological insulator BSTS [11], with the origin explained purely in terms of the intraband harmonic generation mechanism. This explanation, however, cannot be applied here since our observed above-gap harmonics in MoS 2 (gap 1.8 eV) are predominantly generated by the interband mechanism [17,18]. Finally, as mentioned above, the results in Fig.…”

“…Solid-state HHG results from carrier dynamics following the excitation of electrons in the strong field of a laser pulse, and originates from both a nonlinear intraband current and, in case of recombination at high kinetic energies, an interband polarization [14][15][16]. HHG from atomically thin semiconductors such as some of the transition metal dichalcogenides (TMDs) have gained special interest [5,[17][18][19][20][21][22]. In addition to their interesting fundamental properties and their potential applications for optoelectronics and spintronics [23], TMDs are ideal for investigating the microscopic origin of HHG due to the absence of laser propagation effects in the material [15,24,25].…”

Characterizing Anomalous High-Harmonic Generation in Solids

“…We judge the transition energy E h to be material dependent and governed by the particular band structure and coupling matrix elements of the system, but nonetheless expect it to be generally smaller than the gap energy, as above-band-gap harmonics generally proceeds via interband coherences [60,63]. Figure 2 clears up the recent contention on the origin of the perpendicular harmonics in MoS 2 in terms of either anomalous [25,35,64] or interband harmonics [34][35][36][37][38]64]: these two harmonic contributions dominate in different laserparameter and harmonic-energy regimes.…”

“…In addition, it can be easily shown that the oft-used expression for the "interband" current N −1 m =n,k pk mn (t)ρ k nm (t) equals j pol (t) + j anom (t) + j mix (t). In this sense, the experimentally measured perpendicular harmonics from the literature interpreted as "interband" [33][34][35][36][37][38] likely already contains the anomalous contribution, while in this work interband current refers to j pol (t) of Eq. (1b) [60].…”

“…In recent experimental works using linearly polarized drivers, the measured perpendicular-polarized harmonics have frequently been attributed entirely to the anomalous HHG mechanism [15,[25][26][27]. In principle, however, no symmetry rule [32] prohibits the generation of perpendicular-polarized interband harmonics, as has been advocated in several recent works [33][34][35][36][37][38]. A theoretical framework that consolidates these different interpretations of the perpendicular harmonics would be highly desired, and would facilitate the rigorous isolation of the anomalous HHG contribution through its characteristic signatures in the spectral and temporal domains.…”