Investigation Of Frustrated System Based On Slave-boson Mean-field Theory

Geometrically frustrated lattices have exotic quantum states and rich phase dia-grams since the antiparallel alignment of adjacent spins cannot be fully satisfied due to the energy competing.Among of them the Shastry-Sutherland lattice(SSL)is one of the simplest systems,which alternates diagonal links located on a square lattice.Various an-alytical methods and numerical techniques have been employed to study the SSL.From the viewpoint of localized two dimensional Heisenberg Hamiltonian,the original paper gave an exactly analytical solvable ground state,which is the production of valence-bond dimer singlets on the disjointed diagonal links when the ratio of exchange coupling on diagonal bonds and that on x-axes ?=Jdiag/Jx>1.5.While for small ?,the Neel states will become the ground state since a SSL tends to degenerate to square lattice.Between the dimer-singlet state and the Neel state,many intermediate phases and the magnetization plateaus have also been reported.The frustrated materials hosting flat-band structures,like Lieb lattice and Kagome lattice,have been investigated theoretically and even synthesized with unpredicted prop-erties.Recent experiments also showed that twisted bilayer graphene sheets presented a Mott-like insulator owing to the strongly correlated electronic phases.These reports mo-tivated us to investigate the insulator-metal transition in the antiferromagnetic frustrated SSL in this thesis.By using the strongly correlated tl-J1-t2-J2 model in the framework of Slave-Boson mean-field theory,we investigated the band structure,Fermi surface topology,number of mobile chargers of SSL system and its phase diagram systematically for finite tempera-ture and finite doping.The strongly correlated interactions well separate the electronic bands into two sub-sets,and the top of lower band is a quasi-flat band,which localizes electrons below the Fermi level.At small doping,the system is quite generally in the spin density wave(SD-W)insulating phase.For large doping,the system becomes metallic phase with distinct Fermi surface.If the metallic phase has finite magnetic order,it may be defined as SDW metallic phase;otherwise it is paramagnetic metallic phase.The significant roles of the second nearest neighbor parameters t2,J2 and the tem-perature T are revealed,which weakly modify the SDW insulating phase while shrink the area of the SDW metallic phase.As far as we know,a comprehensive understanding of insulator-metal transition of SSL model based on the extended t-J model is still missing.Detail investigations of the phase diagram dependence on the doping,temperature,hopping and exchange coupling will provide a useful theoretical guidance in the investigation of such flat-band and correlated materials.