Making artificial $\textit{p}_{x,y}$-orbital honeycomb electron lattice on metal surface
We theoretically demonstrate that the desired $p_{x,y}$-orbital honeycomb electron lattice can be readily realized by arranging CO molecules into a hexagonal lattice on Cu(111) surface with scanning tunneling microscopy (STM). The electronic structure of the Cu surface states in the presence of CO molecules are calculated with various methods, i.e. muffin-tin potential model, tight-binding model, and DFT simulations. We show that, by measuring the LDOS pattern using STM, the $p$-orbital $\sigma$ bonds and anti-bonding $\sigma$ bonds can be identified in experiment. Meanwhile, different from the case of graphene, the $p$-orbital honeycomb lattice has two kinds of edge states, which can also be directly observed in STM experiment. Our work first points out a feasible way to construct a $p_{x,y}$-orbital honeycomb electron lattice in real system, which may have exotic properties, such as Wigner crystal, ferromagnetism, $f$-wave superconductivity and QAH effect. Furthermore, considering the recent works about $p$-orbital square lattice in similar systems [M. R. Slot, et al. Nat. Phys. 13, 672 (2017); Liang Ma, et al. arXiv:1707.04756], our work once again illustrates that the artificial electron lattice on metal surface is an ideal platform to study the orbital physics in a controllable way.