Effective gauge-field theory of thet−Jmodel in the charge-spin separated state and its transport properties

We study the slave-boson t-J model of cuprates with high superconducting transition temperatures, and derive its low-energy effective field theory for the charge-spin separated state in a self-consistent manner. The phase degrees of freedom of the mean field for hoppings of holons and spinons can be regarded as a U(1) gauge field, Aᵢ. The charge-spin separation occurs below a certain temperature, TCSS, as a deconfinement phenomenon of the dynamics of Aᵢ. Below a certain temperature TSG(<TCSS), the spin-gap phase develops as the Higgs phase of the gauge-field dynamics, and Aᵢ acquires a mass mA. The effective field theory near TSG takes the form of a Ginzburg-Landau theory of a complex scalar field λ coupled with Aᵢ, where λ represents d-wave pairings of spinons. Three dimensionality of the system is crucial to realize a phase transition at TSG. By using this field theory, we calculate the dc resistivity ρ. At T>TSG, ρ is proportional to T. At T<TSG, it deviates downward from the T-linear behavior as ρ∝T1-c(TSG-T)ᵈ. When the system is near (but not) two dimensional, due to the compactness of the phase of the field λ, the exponent d deviates from its mean-field value $1/2$ and becomes a nonuniversal quantity which depends on temperature and doping. This significantly improves the comparison with the experimental data.