Theory of the Normal State of Cuprate Superconducting Materials

We have proposed a model Hamiltonian, which describes a simple physical picture that the holes with single occupation constraint introduced by doping move in the antiferromagnetic background of the copper spins, to describe the normal state of the cuprate superconducting materials, and used the renormalization group method to calculate its anomalous magnetic and transport properties. The anomalous magnetic behavior of the normal state is controlled by both the copper spin and the spin part of the doping hole residing on the O sites. The physical resistivity is determined by both the quasiparticle-spin-fluctuation and the quasiparticle-gauge-fluctuation scatterings and the Hall coefficient is determined by the parity-odd gauge interaction deriving from the nature of the hard-core boson which describes the charge part of the doping holes. PACS numbers: 74.20.Mn, 75.10.Jm, 75.40.Gb. 1 Since the discovery of the cuprate superconducting materials there has still considerable controversy over the choice of the appropriate microscopic Hamiltonian. Although there have appeared a lot of models, for example, the one-band effective Hubbard model, t-J model, three-band Hubbard model, phenomenological marginal Fermi liquid, nearly antiferromagnetic Fermi liquid and so on, to try to describe the normal and superconducting states of the cuprate superconducting materials, it is generally agreed now that Anderson’s starting point, namly, strongly on site Coulomb interactions among a partially filled band of Cu 3d level, is correct. The controversial point is that one is how to treat doping holes residing on O 2p level. At zero doping, it is generally agreed that the insulating ”parent” phases of the cuprate materials are charge-transfer insulators and can be described by quantum antiferromagnetic Heisenberg model. Substantial progress has been achieved in understanding of the Heisenberg limit, both theoretically and experimentally. Under a finite doping range, Zhang and Rice showed that the three-band Hubbard model can be reduced into a single band effective Hamiltonian–the t-J model under the case of spin singlet phase that hybridization strongly binds a hole on each square of O atoms to the central Cu ions in a similar way as a hole in the single band effective Hamiltonian, then two holes feel a strong repulsion against residing on the same square. In fact, in this representation, the doping hole residing on the O site