  Two-dimensional checkerboard lattice, the simplest line-graph lattice, has
been intensively studied as a toy model, while material design and synthesis
remain elusive. Here, we report theoretical prediction and experimental
realization of the checkerboard lattice in monolayer Cu$_2$N. Experimentally,
monolayer Cu$_2$N can be realized in the well-known N/Cu(100) and N/Cu(111)
systems that were previously mistakenly believed to be insulators. Combined
angle-resolved photoemission spectroscopy measurements, first-principles
calculations, and tight-binding analysis show that both systems host
checkerboard-derived hole pockets near the Fermi level. In addition, monolayer
Cu$_2$N has outstanding stability in air and organic solvents, which is crucial
for further device applications.
