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 is calculated with various methods, \textit{i.e.}~DFT simulations, muffin-tin potential model and tight-binding model. Our calculations indicate that, by measuring the LDOS pattern using STM, the $p$-orbital surface bands can be immediately identified in experiment. We also give an analytic interpretation of the $p$-orbital LDOS pattern with $k \cdot p$ method. 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 points out a feasible way to construct a $p_{x,y}$-orbital honeycomb electron lattice in a real system, which may have exotic properties, such as Wigner crystal, ferromagnetism, $f$-wave superconductivity, quantum anomalous Hall (QAH) effect. Furthermore, we also propose a simple way to calculate and identify the modified Cu surface bands in the Cu/CO systems with the DFT simulations. Considering the recent works about $p$-orbital square lattice in similar systems [M. R. Slot, \textit{et al.} Nat. Phys. \textbf{13}, 672 (2017); Liang Ma, \textit{et al.} Phys. Rev. B \textbf{99}, 205403 (2019)], 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.