Lattice imperfections and high-harmonic generation in correlated systems

We study effects of lattice imperfections on high-harmonic generation from correlated systems using the Fermi–Hubbard model. We simulate such imperfections by randomly modifying the chemical potential across the individual lattice sites. We control the degree of electron–electron interaction by varying the Hubbard U . In the limit of vanishing U , this approach results in Anderson localization. For nonvanishing U , we rationalize the spectral observations in terms of qualitative k -space and real-space pictures. When the interaction and imperfection terms are of comparable magnitude, they may balance each other out, causing Bloch-like transitions. If the terms differ significantly, each electron transition requires a relatively large amount of energy and the current is reduced. We find that imperfections result in increased high-harmonic gain. The spectral gain is mainly in high harmonic orders for low U and low orders for high U .