Theoretical Study Of Artificial Two-dimensional Electron Lattice Based On Metal Surface State

Artificial quantum lattice is the basis of quantum simulation,and has attracted extensive attentions in various fields of physics in the last two decades.The main reason is that we can simulate some complex and novel quantum states in the artificial quantum lattice.Using atomic manipulation techniques,artificial electron lattice constructed by molecule adsorption on metal surface is a new class of artificial quantum lattice.Compared to other artificial quantum lattice systems,such system has many advantages.An important question,then,is whether this system can be used to achieve more interesting and complex quantum lattices.In our thesis,inspired by this important issue,we theoretically and systematically study the construction scheme of novel and complex quantum lattices.Our main results are as follows:（1）We propose the experimental scheme of Lieb electron lattice in Cu/CO system.Lieb lattice is one of the most typical two-dimensional lattice with a flat band,which could induce exotic strong correlation and topological effects.Previous experimental schemes for Lieb lattices are based on Boson systems such as cold atom systems and photonic crystals,but there is no experimental scheme to realize the Lieb lattice of Fermion system so far.In this work,a unique CO lattice is designed based on Cu/CO adsorption system.Our theoretical calculations show that this CO lattice can transform the Cu（111）surface states into Lieb electron lattice.（2）We further demonstrate that in such a artificial quantum lattice system,the concept of atomic orbital still holds.Based on the p orbital concept,we theoretically explain the complex electron distribution image in the high energy region of Lieb lattice,which has been observed in recent experiment.（3）Based on artificial p orbital concept,we further propose an experimental scheme to realize the p_x,y-orbital honeycomb electron lattice.All the studies of p_x,y-orbital honeycomb lattice of Fermion system are limited to theory so far.The main reason is that no appropriate experimental system has been found.By theoretical calculations,we demonstrate that p_x,y-orbital honeycomb electron lattice can be realized in Cu/CO system by designing appropriate adsorption configuration of CO molecules.（4）The Cu/CO system is a quantum antidot system,where CO molecules apply a repulsive potential to the electrons of surface states.In fact,there is another way to construct an artificial electron lattice,which is to construct it directly from the adsorbed atoms themselves.Using a simple two-dimensional SSH（Su-Schrieffer-Heeger）model as an example,we construct a second-order topological insulator with Au as adsorbed atoms,and verify the feasibility of this scheme to construct artificial topological lattices.By density functional theory（DFT）calculations,we demonstrate that the emergence of topological corner states can be confirmed experimentally by measuring the surface electron distribution with scanning tunneling microscope（STM）.Besides a series of work on artificial electron lattices,I develop a numerical method starting from the DFT calculations to efficiently search for all possible multipolar order parameters in materials.At present,the study of multipolar order parameters is faced with great challenges both in experimental characterization and theoretical calculations.In theory,there is a lack of fast and effective methods to predict and calculate multipolar order parameters starting from DFT.In this work,we achieve a methodological breakthrough.We apply this new method to the monolayer d electron system with honeycomb structure and find two pure metastable magnetic octupolar states.