We study interference patterns and Friedel oscillations (FO) due to scattering from two or more localized impurities and scattering from extended inhomogeneities in the two-dimensional lattice systems of interacting fermions. Correlations between particles are accounted for by using an approximate method based on the real-space dynamical mean-field theory and a homogeneous self-energy approximation (HSEA), where the site-dependent part of the self-energy is neglected. We find that the interference maxima and minima change systematically as we vary the relative distance between the two impurities. At the same time, the increase of the interaction does not shift the position of interference fringes but only reduces their intensities. A comparison with the single impurity cases clearly shows complex patterns in FO fringes induced by additional multiple scattering processes. In the case of an extended steplike potential the system becomes more homogeneous when the interaction increases. FO and interference patterns are not present in the Mott insulating phase in both single and many impurity models.

• Received 22 July 2020
• Revised 9 May 2022
• Accepted 10 June 2022

DOI:https://doi.org/10.1103/PhysRevB.105.235129