Wannier quasi-classical approach to high harmonic generation in semiconductors

Abstract

An intuitive and complete understanding of the underlying processes in high harmonic generation (HHG) in solids will enable the development and optimization of experimental techniques for attosecond measurement of dynamical and structural properties of solids. Here we introduce the Wannier quasi-classical (WQC) theory, which allows the characterization of HHG in terms of classical trajectories. The WQC approach completes the single-body picture for HHG in semiconductors, as it is in quantitative agreement with quantum calculations. The importance of WQC theory extends beyond HHG; it enables modeling of dynamic processes in solids with classical trajectories, such as for coherent control and transport processes, potentially providing better scalability and a more intuitive understanding.

Mechanisms of high harmonic generation in solids

“…( 13) is compared; HHG for N = 1, 3 is non-resonant and turns resonant for N > 5; the first above bandgap harmonic is N = 9. Above minimum bandgap harmonics are resonant, in agreement with previous theoretical [29][30][31][32]34] and experimental [22,24,42] work.…”

“…The prevalent assumption is that HHG is driven by resonant mechanisms. Laser induced electron-hole pair creation is followed by HHG via interband polarization buildup in (ii) [22,24,[29][30][31][32]34], or via the intraband nonlinearity of individual bands in (iii) [3,4].…”

High harmonics from backscattering of delocalized electrons

“…The so-called "three-step model" [5] is key to understand the microscopic electron dynamics of HHG in atoms and molecules semiclassically in terms of classical trajectories [6]. It has been adapted successfully for interband HHG in solids [7][8][9], suggesting that fundamental properties of high harmonics are ruled by the same basic principles from atoms to the solid state. On the other hand, a solid-state environment should offer more possibilities to influence these phenomena than an atom due to the larger structural complexity and variability [10][11][12][13][14].…”

Expanded view of electron-hole recollisions in solid-state high-order harmonic generation: Full-Brillouin-zone tunneling and imperfect recollisions

“…It should be mentioned that recent progress [17,39,57] has been made towards solving the saddle point equations (5) and performing the stationary phase approximation on the integral in Eq. (3).…”

“…While the SBEs and TD-DFT methods are able to accurately simulate the HHG process, they can be regarded as numerical experiments that contain all the relevant physics, and the underlying physical pictures can be difficult to extract. For this reason the celebrated gas-phase three-step model [35,36] has been generalized to solids [37][38][39], and has been shown to provide an intuitive real-space picture for the interband harmonics: an electron-hole pair is created when the external field causes an electron to tunnel from the valence band to the conduction band at the minimum band gap; the electron and hole are driven apart by the laser; they can recollide when they spatially reencounter each other, leading to the emission of harmonic radiation. The recollision picture has been instrumental in our fundamental understanding of solid-state HHG [2,17,37,38,40,41], as well as other related nonlinear phenomena such as high-order-sideband generation [42][43][44][45][46].…”