Crystal-momentum-resolved contributions to multiple plateaus of high-order harmonic generation from band-gap materials

Abstract

We study the crystal-momentum-resolved contributions to the high-order harmonic generation (HHG) in band-gap materials, and identify the relevant initial crystal momenta for the first and higher plateaus of the HHG spectra. We do so by using a time-dependent density-functional theory model of one-dimensional linear chains. We introduce a self-consistent periodic treatment for the infinitely extended limit of the linear chain model, which provides a convenient way to simulate and discuss the HHG from a perfect crystal beyond the single-active-electron approximation. The multiplateau spectral feature is elucidated by a semiclassical k-space trajectory analysis with multiple conduction bands taken into account. In the considered laser-interaction regime, the multiple plateaus beyond the first cutoff are found to stem mainly from electrons with initial crystal momenta away from the point (k = 0), while electrons with initial crystal momenta located around the point are responsible for the harmonics in the first plateau. We also show that similar findings can be obtained from calculations using a sufficiently large finite model, which proves to mimic the corresponding infinite periodic limit in terms of the band structures and the HHG spectra.

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

“…While much of the microscopic HHG dynamics can be understood in terms of a two-band picture [14,16,17,21,[32][33][34] involving a filled valence band and a single conduction band, a number of works have highlighted the role of multiple bands [19,[35][36][37][38][39]. In particular, it has been experimentally demonstrated that multiple bands were responsible for nonintuitive harmonic waveforms in bulk GaSe [40], the emergence of multiple plateaus in rare-gas solids [41], and yield enhancement of different harmonic regions in MgO [42].…”

High harmonics from backscattering of delocalized electrons

“…where J tot (t) is the total current in the system and W (t) is a window function of the laser-pulse-envelope shape for improving the signal-to-noise ratio. Details of the methods and parameters used as well as the periodic treatment for the limit N →∞ can be found in [19]. The laser pulse with frequency ω 0 is linearly polarized along the chain and described in dipole approximation by the vector potential A(t) = A 0 sin 2 (ω 0 t/[2n cyc ]) sin(ω 0 t) for 0 ≤ t ≤ 2πn cyc /ω 0 and A(t) = 0 otherwise.…”

Enhanced high-order harmonics through periodicity breaks: from backscattering to impurity states

“…HHG in a condensed-matter environment shares similarities with its well-known counterpart in atoms and molecules, but also differences and richer physics due to the larger structural complexity and variability [9][10][11]. For example, the solidstate HHG cutoff was found to scale quasi-linearly with the driving field strength rather than quadratically as in atoms and molecules [1,[12][13][14]; under suitable conditions, solidstate HHG spectra exhibit multiple plateaus due to the multiple conduction bands [9,[15][16][17]. The physical mechanism underlying HHG from solids, although still being lively discussed from different perspectives [18][19][20][21][22][23][24][25], is typically described within a band picture in terms of intra-and interband processes [2,3,18] acknowledging the delocalized nature of the participating electrons.…”