Superfluid States In ?-T₃ Lattice

The discovery of graphene is of great significance to the development of condensed matter physics.Since the development of extraction methods of graphene monolayer,many researchers are absorbed in the study of this material.The reason for a lot of research on graphene is its special properties.This material has very high strength.Although it is very thin,its carriers still have great mobility and conductivity with zero effective mass.Graphene has many latent applications in modern electronic equipments,due to the limitation of large-scale preparation technology,its effective application has been hindered.For example,(1)the production cost of commercial scale is very large?(2)the energy bands of graphene are gapless,so different technologies should be used to open the gap between the conduction band and the valence band?(3)It is hard to get a big piece of graphene.Due to these limitations,researchers are looking for new materials similar to graphene.The honeycomb lattice structure of graphene provides a favorable reference for the study of other new models.In the process of looking for two-dimensional new materials similar to graphene,people have done a lot of research,and finally found?-T₃lattice,which is similar to graphene in many aspects,but also has some characteristics different from graphene.Now people turn their attention to develop its characteristics.Because it has amazing basic physical phenomena,and has a wide application future in solid-state devices.Researchers have done a lot of work in this area,such as Hofstadter butterfly effect,magneto-optical conductivity,Klein tunneling effect,Zitterbewegung effect and so on.The physical properties of?-T₃lattice is alays a research hot topic.In this paper,we study the superfluid state of the Hubbard model with attractive interaction in?-T₃lattice.It is found that due to the existence of three sublattices,three non-zero superfluid order parameters are usually used to characterize the superfluid state.When the two hopping amplitudes(between different lattices)are equal,the system has particle-hole symmetry,and the flat band plays an vital role in the nearly half-filling superfluid pairing.For example,when the filling factor falls in the flat band,the larger density of states in the flat band is beneficial to the superfluid pairing,and the superfluid order parameter reaches a larger value.When the filling factor is between the flat band and conduction band,the superfluid order parameter is very small due to the density of states are zero.With the increase of filling factor,the superfluid order parameter exhibits nonmonotonic behavior.Finally,we also study the change of the edge states with the interaction U and the coupling parameter?under the open boundary condition.The results show that there are some interesting edge states in the middle of the quasiparticle band,which are compared with the case of graphene.