  The electronic properties of solids are determined by the crystal structure
and interactions between electrons, giving rise to a variety of collective
phenomena including superconductivity, strange metals and correlated
insulators. The mechanisms underpinning many of these collective phenomena
remain unknown, driving interest in creating artificial crystals which
replicate the system of interest while allowing precise control of key
parameters. Cold atoms trapped in optical lattices provide great flexibility
and tunability [1, 2], but cannot replicate the long range Coulomb interactions
and long range hopping that drive collective phenomena in real crystals. Solid
state approaches support long range hopping and interactions, but previous
attempts with laterally patterned semiconductor systems were not able to create
tunable low disorder artificial crystals, while approaches based on Moire
superlattices in twisted two-dimensional (2D) materials [3, 4] have limited
tunability and control of lattice geometry. Here we demonstrate the formation
of highly tunable artificial crystals by superimposing a periodic electrostatic
potential on the 2D electron gas in an ultrashallow (25 nm deep) GaAs quantum
well. The 100 nm period artificial crystal is identified by the formation of a
new bandstructure, different from the original cubic crystal and unique to the
artificial triangular lattice: transport measurements show the Hall coefficient
changing sign as the chemical potential sweeps through the artificial bands.
Uniquely, the artificial bandstructure can be continuously tuned from parabolic
free-electron bands into linear graphene-like and flat kagome-like bands in a
single device. This approach allows the formation arbitrary geometry 2D
artificial crystals, opening a new route to studying collective quantum states.
