Realization of a two-dimensional checkerboard lattice in monolayer Cu$_2$N
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.