  This work considers a two-dimensional artificial triangular anti-dot lattice
(TAL); a semiconductor based artificial crystal hosting Dirac cones, flat bands
and Fermi surface nesting. All such single particle features have dramatic
implications for the emergent correlated phases. This work predominantly
focuses on the existence of a robust flatband and enumerates the possible
correlated phases that follow. We find that the flatband is generated, in the
single-particle theory, when charges align themselves along a kagome lattice
with the same period as the TAL. The correlated phases are studied using
complementary techniques of expansions in strong and weak Coulomb interaction.
Our microscopic modelling shows that for the purpose of generating strongly
correlated phases, hole doped TALs have significant advantages over electron
doped.
