  Long-lived and ultra-confined plasmons in two-dimensional (2D) electron
systems may provide a sub-wavelength diagnostic tool to investigate localized
dielectric, electromagnetic, and pseudo-electromagnetic perturbations. In this
Article, we present a general theoretical framework to study the scattering of
2D plasmons against such perturbations in the non-retarded limit. We discuss
both parabolic-band and massless Dirac fermion 2D electron systems. Our theory
starts from a Lippmann-Schwinger equation for the screened potential in an
inhomogeneous 2D electron system and utilizes as inputs analytical
long-wavelength expressions for the density-density response function, going
beyond the local approximation. We present illustrative results for the
scattering of 2D plasmons against a point-like charged impurity and a
one-dimensional electrostatic barrier due to a line of charges. Exact numerical
results obtained from the solution of the Lippmann-Schwinger equation are
compared with approximate results based on the Born and eikonal approximations.
The importance of nonlocal effects is finally emphasized.
