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

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 defect-state orbitals in the HHG process is investigated for different realizations of the linear chain and laser parameters.