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 $U$.