Design And Modulation Of Two-Dimensional Nodal-Loop Materials

In recent years,nodal-line semimetals（NLSM）have attracted a lot of attention due to their research in fundamental physics and potential applications in the next generation of nanoscale spintronic devices.Unlike the discrete points in Dirac/Weyl semimetals,nodal-line semimetals form continuous open or closed loops in momentum space that are protected by certain crystal symmetry.There are gapless band crossings in nodal-line semimetals,and this unique energy band crossing is associated with many exotic physical phenomena,such as drumhead surface states,high-temperature surface superconductivity and anomalous quantum oscillation.So far,three-dimensional（3D）nodal-line semimetals have been demonstrated theoretically or experimentally,such as Ti₃Al,Cu₃Pd N and Ti B₂,while the exploration of two-dimensional（2D）nodal-line semimetals is still challenging because of the reduced crystal symmetry compared to the 3D case.Some 2D monolayers,such as Si-Cmma,B₂O,Ta Si Te₆ and Mn B are theoretically predicted to be nodal-line semimetals,and some of them,such as Cu₂Si,Cu Se and Ga Ag₂,have been successfully synthesized experimentally and verified by ARPES as nodal-line semimetals.It is worth mentioning that the gapless nodal-line of most of the above mentioned 2D nodal-line semimetal candidates are protected by horizontal mirror symmetry,and this symmetry protection mechanism has recently been extended to nonsymmorphic glide mirror symmetry,for example in Mn NF and Ni B₂ monolayer.So far,the number of known 2D nodal-line semimetal materials is still limited.Therefore,it is urgent and meaningful to search for novel 2D nodal-line semimetal materials,to propose new mechanisms for 2D nodal-line symmetry protection,and to design efficient and versatile spintronic devices.So far most of the 2D nodal-line semimetal materials are protected by horizontal mirror symmetry,and there are few nodal-line semimetal materials protected by nonsymmorphic glide mirror symmetry,and there is no clear physical understanding of the mechanism of symmetry protection.We systematically use first-principles calculations to predict a 2D nodal-line semimetal,Al Sb,whose conduction and valence bands cross each other to form a singular nodal-line state.By means of charge differential density（CDD）and electronic localization function（ELF）,we explain the mechanism for the existence of excellent electrical conductivity in Al Sb monolayers.We use a symmetry-constrained six-band tight-binding model to demonstrate that the nodal-line states in Al Sb monolayers are protected by glide mirror symmetry.In addition,we propose a method to protect and break the nodal-line state experimentally using the symmetry protection mechanism.Our study not only provides a two-dimensional nodal-line semimetal candidate with a new symmetry protection mechanism,but also establishes a physical model to explain the symmetry protection mechanism.Since most of the nodal-line state materials are three-dimensional and very few two-dimensional nodal-line state materials have been synthesized experimentally,we expect to construct physical models to predict new 2D nodal-line semimetal and provide new ideas for experimental synthesis.Lieb lattice is named by Elliott H.Lieb,an American mathematical physicist,and various exotic quantum states have been proposed in this configuration,such as ground state ferromagnetism,superconductivity and topological states.We have constructed a tight-binding model based on the Lieb lattice,demonstrated the possibility of the existence of nodal-line states in the Lieb lattice,and found a practical material Zn₂C monolayer with the characteristics of the Lieb lattice by first-principles calculations,and demonstrated the stability of its thermal,dynamic,and mechanical properties.By calculating the energy band structure of its electrons,it is found that the nodal-line states exist around the R point near the Fermi surface and maintain gapless under tensile and compressive strains,proving its robustness in a practical environment.In recent years,the research of antiferromagnetic materials has become a hot topic because they have the advantages of high interference resistance and low energy consumption compared with ferromagnetic materials.However,there are very few studies on antiferromagnetic nodal-line semimetals,so we expect to design a physical model of antiferromagnetic nodal-line semimetal and find a practical material that can have this property.We added one site to the conventional Lieb lattice and named it Lieb-like lattice.By constructing a tight-binding model,we argued the possibility of the existence of the antiferromagnetic nodal-line state in this configuration.At the same time,we found an actual material Co N₂ monolayer by using first-principles calculations,and found that its electron energy band structure has a nodal-line around thepoint,and judged that its ground state is an antiferromagnetic state by constructing several different magnetic configurations.This work not only designs a physical model of the antiferromagnetic nodal-line state,but also predicts a practical material,providing a new platform for the study of the antiferromagnetic nodal-line semimetals.This paper provides a new approach and direction for the design and regulation of the nodal-line semimetal materials by systematically investigating the possibility of the existence of the nodal-line state in various models and the symmetry protection mechanism of the nodal-line state.