  Electrostatic confinement in semiconductors provides a flexible platform for
the emulation of interacting electrons in a two-dimensional lattice, including
in the presence of gauge fields. This combination offers the potential to
realize a wide host of quantum phases. Here we present a measurement and
fabrication scheme that builds on capacitance spectroscopy and allows for the
independent control of density and periodic potential strength imposed on a
two-dimensional electron gas. We characterize disorder levels and
(in)homogeneity and develop and optimize different gating strategies at length
scales where interactions are expected to be strong. A continuation of these
ideas might see to fruition the emulation of interaction-driven Mott
transitions or Hofstadter butterfly physics.
