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High-Harmonic Generation (HHG) in solids has attracted great attention in recent years as it represents a promising tool to probe the structure, topology, and ultrafast dynamics of condensed matter systems. We report on our recent theoretical findings on the microscopic generation mechanisms behind HHG. We show that the interband HHG mechanism pictured by the three-step model involving electron-hole-pair creation, propagation and recollision should be greatly expanded to encompass general cases: often the electron-hole pairs created away from the minimal band gap can dominate the HHG emission, and the electron-hole pair can undergo imperfect recolliions, i.e. recollisions where the electron and hole do not exactly overlap spatially. We further characterize the anomalous HHG mechanism in solids, i.e. the perpendicular-polarized harmonics generated by the contribution of the Berry curvatures and the anomalous velocities. We find that the anomalous harmonics will in general be competing with the interband harmonics, and state general situations where one dominates over the other. This resolves a recent debate on the origin of the perpendicular-polarized harmonics.
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