  Studying the electronic structure of defects in materials is an important
subject in condensed matter physics. From a mathematical point of view,
nonlinear mean-field models of localized defects in insulators are well
understood. We present here a mean-field model to study a particular instance
of extended defects in metals. These extended defects typically correspond to
taking out a slab of finite width in the three-dimensional homogeneous electron
gas. We work in the framework of the reduced Hartree-Fock model with either
Yukawa or Coulomb interactions. Using techniques developed in~[Frank2011,
Frank2013] to study local perturbations of the free-electron gas, we show that
our model admits minimizers, and that Yukawa ground state energies and density
matrices converge to ground state Coulomb energies and density matrices as the
Yukawa parameter tends to zero. We moreover present numerical simulations where
we observe Friedel oscillations in the total electronic density.
