Limitations of the single-active-electron approximation in quantum simulations of solid high-order harmonic generation

Crystal-momentum-resolved contributions to high-order harmonic generation in solids

“…Over the range of displayed electric-field strengths the intraand interband spectra are dominated by odd harmonics, with slim traces of even harmonics. Small even and noninteger HHG yields were also noticed in an SBE-based calculation by Li et al [23] and explained in terms of the combined effect of the external-field and time dependence of the TDM D vc κ (t ) . We speculate that this effect may be enhanced due to our inclusion of the term defined by Eq.…”

“…In particular, we find that HHG spectra calculated by only including the initial crystal momentum at the center of the BZ (the point) [8] noticeably differ from calculations that include initial crystal momenta in the entire BZ [9], as previously pointed out by Floss et al [31]. It has been recently proposed that the range of crystal momenta used in SAE calculations should be used as an adjustable parameter for getting converged numerical HHG spectra [23]. In the present work we revisit this suggestion and analytically determine, based on a saddle-point approximation, the range of initial crystal momenta needed for the computation of HHG spectra at a given accuracy.…”

“…Both, the SBE model for HHG in Refs. [9,23,29] and the expansion of TSDE solutions in a Houston basis, use an adiabatic basis. Note that the SBE model in Refs.…”

“…Note that the SBE model in Refs. [9,23,29] adds the damping term ρ cv k (t )/T 2 to Eq. (21), with an adjustable damping time T 2 for the interband coupling [34].…”

“…Compared to HHG in atomic gases, theoretical investigations of solid HHG have indicated striking new effects, such as multiple plateaus [8,20] in HHG spectra and a linear dependence of the HHG cutoff frequency on the peak electric-field strengths of the driving laser [8,[21][22][23]. These characteristics have been revealed by numerically solving either the time-dependent Schrödinger (TDSE) in single-active-electron (SAE) approximation [8,[23][24][25] or semiconductor Bloch equations (SBEs) [9,23,[26][27][28][29][30][31]. SAE-TDSE-based numerical models have employed basis-set expansions of the active electron's wave function using either static [32] or adiabatic [8,33] Bloch states.…”