Designing an artificial Lieb lattice on a metal surface

Recently, several experiments [K. K. Gomes et al., Nature (London) 483, 306 (2012); S. Wang et al., Phys. Rev. Lett. 113, 196803 (2014)] have illustrated that metal surface electrons can be manipulated to form a two-dimensional (2D) lattice by depositing a designer molecule lattice on a metal surface. This offers a promising new technique to construct artificial 2D electron lattices. Here we theoretically propose a molecule lattice pattern to realize an artificial Lieb lattice on a metal surface, which shows a flat electronic band due to the lattice geometry. We show that the localization of electrons in the flat band may be understood from the viewpoint of electron interference, which may be probed by measuring the local density of states with scanning tunneling microscopy. Our proposal may be readily implemented in experiment and may offer an ideal solid state platform to investigate the novel flat band physics of the Lieb lattice.