Properties Of Hexagonal Lattice Structures

The optical lattice,which is pure and highly adjustable,is a periodic potential well prepared by a standing wave field.The optical lattice that can be used to simulate the solid lattice system is an effective quantum simulator in the research field of multi-body strongly correlated interaction in condensed matter physics.The spin-orbit coupling effect in optical lattices leads to new quantum states,which has potential applications in quantum computation and quantum simulation.Different types of optical lattices can be prepared by different angles of the standing wave field.Among these types,the hexagonal optical lattice is composed of two triangular sub-lattices with different spins,which can be used to research the dispersion relations of Dirac points and the artificial relativistic effect.Moreover,the application of artificial gauge potentials in hexagonal optical lattices will lead to the occurrence of quantum anomalous Hall effects and various quantum phase transitions.Similarly,graphene has a hexagonal lattice structure in solid materials.Graphene has a linear crossover band structure near Dirac points,showing special transport properties.The graphene nanoribbon “cut”out from graphene is a quasi-one-dimensional material whose properties depend largely on the edge type and has a wide range of applications in spintronics.Particles in a hexagonal lattice have special physical properties.Quantum Hall effect and topology have been found in both hexagonal graphene and hexagonal optical lattice systems,indicating that many commonalities exist between the two systems.In the process of preparing graphene in the experiment,various defects exist and have a great impact on the electronic properties of graphene.However,the perfect structure of the hexagonal optical lattice can well simulate the physical properties of the ideal graphene,which helps to discover different effects in the graphene system.The study of quantum phase transitions in hexagonal optical lattices helps the understanding of phase transition characteristics of graphene systems.Additionally,most of the novel phenomena in optical lattices can be traced to solid lattice systems.Therefore,the research of hexagonal graphene helps to explore more effects in the hexagonal optical lattice.This paper discusses the properties of hexagonal lattice structures from two perspectives.(1)We discover the unzipping rules of single-walled carbon nanotubes,and generalize the concept of the chiral graphene nanoribbons.We research the edge magnetism of generalized chiral graphene nanoribbons and the induce effect of single vacancy defects on the edge magnetism.(2)We introduce the preparation method of hexagonal optical lattices and the quantum phase resulting from the interaction between different spin states and spin-dependent lattice potentials.We describe the modulation effect of the hexagonal optical lattice to the critical point of quantum phase transition.