Orbital degree of freedom in artificial electron lattices on metal surface
Orbital degree of freedom plays a fundamental role in condensed matter physics. Recently, a new kind of artificial electron lattice has been realized in experiments by confining the metal surface electrons with adsorbed molecular lattice. A most recent example is the Lieb lattice realized by CO adsorption on Cu(111) surface [M. R. Slot, et al., Nat. Phys. 13, 672(2017)]. The Lieb lattice is of special interest due to its flat band physics. Here, by first-principles calculations, muffin-tin potential model and tight binding model, we demonstrate that, the high energy states observed in the experiment actually correspond to the artificial $p$-orbitals of the electron lattice. Our numerical results, together with the experimental observation, show that artificial $p$-orbital fermionic lattice has already been realized in solid state system. This opens a new avenue to investigate the orbital degree of freedom in a controllable way.