Effects of vacancies on high-order harmonic generation in a linear chain with band gap

Abstract

High-order harmonic generation (HHG) in imperfect lattices with point defect vacancies is studied using a self-consistent time-dependent density-functional approach for a one-dimensional linear chain with a band gap. Compared with a perfect lattice with no vacancies, the HHG yield decreases by increasing the number of evenly distributed vacancies but remains almost unchanged in the case when vacancies are localized at neighboring lattice points. By introducing atomic-type point vacancies in the linear chain, it is effectively partitioned into several subsystems and the overall shape of HHG spectra of the resulting system can be modeled via the HHG of its subsystems provided each subsystem is large enough to behave like a bulk solid. For sufficiently small subsystems, the HHG spectra show detectable signatures of finite structure but maintains the overall structure of the spectrum of a bulk solids. A time-frequency profile of the emitted harmonics shows less regular sinusoidal patterns in the systems with vacancies compared with the perfect lattice. The role the vacancy-induced defectstate orbitals in the HHG process is investigated for different realizations of the linear chain and laser parameters.

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

“…In this work we set Z = 4, a = 7, and = 2.25, as in Refs. [49,50,53,55]. For sufficiently large N, this model can qualitatively represent a bulk solid with two fully occupied valence bands.…”

“…Let us first revisit the finite chain model and the (TD)DFT approach used in previous works [49,50,53,55]. A theoretical treatment of the corresponding infinitely extended system will be presented in Sec.…”

“…Two main theoretical approaches to study HHG in solids include (i) the time-dependent Schrödinger equation (TDSE) for individual Bloch electrons with specific k values [25][26][27][28][29][30][31][32][33][34][35], and (ii) many-electron approaches such as the semiconductor Bloch equations (SBEs) [36][37][38][39][40][41][42][43][44][45][46] and the time-dependent density-functional theory (TDDFT) [23,[47][48][49][50][51][52][53][54][55][56]. In Ref.…”

“…The response of a range of system sizes, from atomic to bulk solids, was studied with this model to reveal how the harmonic cutoff changes from atomic to solid-state HHG [50]. Due to its flexibility in constructing self-consistent model systems, this methodology was applied to investigate topological edge effects [51,52] and various types of imperfection effects such as doping [53], disorder [52,54], and vacancies [55]. We note that recently such a finite-system model was also used for studying the carrier-envelope-phase effects [60], for examining the phase invariance of the SBEs [61], and for comparing semiclassical trajectory models [62].…”

“…Similar to previous studies [49,50,53,55], here we employ the 1D TDDFT model to study HHG from a linear chain of atoms exposed to linearly polarized laser pulses. In this work, we extend the previous finite-chain model to the corresponding infinitely extended limit with a periodic treatment, and demonstrate that a sufficiently large finite model indeed mimics the infinite periodic limit in terms of band structures and HHG spectra.…”