Abstract:
The Fermi surface calculated within the rotating antiferromagentism theory undergoes a topological change when doping changes from p-type to n-type, in qualitative agreement with experimental data for n-type cuprate Nd$_{2-x}$Ce$_x$CuO$_4$ and p-type La$_{2-x}$Sr$_x$CuO$_4$. Also, the reconstruction of the Fermi surface observed experimentally close to optimal doing in p-type cuprates, and slightly higher than optimal doping in the overdoped regime for this n-type high-$T_C$ cuprate is well accounted for in this theory, and is a consequence of quantum criticality caused by the disappearance of rotating antiferromagnetism. The present results are in qualitative agreement with the recently observed quantum oscillations in some high-$T_C$ cuprates regarding the change in the size of the Fermi surface as doping evolves and the location of its reconstruction. This paper presents new results about the application of the rotating antiferromagnetism theory to the study of electronic structure for n-type materials.

Abstract:
Using the U(1) holon pair slave boson theory [Phys. Rev. B 64, 052501 2001)], we derive a low energy field theory of dealing with both d-wave superconductivity and antiferromagnetism for underdoped cuprates by constructing both the Cooper pair field and the chargon pair field. In terms of the internal gauge field, the Cooper pair field carries no internal charge while the chargon pair field carries the internal charge. They are decoupled in the low energy limit. This allows us to separately treat the XY model of the Cooper pair field to describe superconductivity and the Abelian Higgs model of the chargon pair field to describe antiferromagnetism in the presence of Dirac fermions at and near the d-wave nodal points. Thus we find that the d-wave superconductivity can coexist with antiferromagnetism and that despite the coexistence, the antiferromagnetism can not affect the superconducting transition, thus allowing the XY universality class in the extreme type II limit.

Abstract:
I present a formalism for dealing directly with the effects of the Gutzwiller projection, which is implicit in the t-J model widely believed to underly the phenomenology of the high-Tc cuprates. I suggest that a true BCS condensation from a Fermi liquid state takes place, but in the unphysical space prior to projection. The theory which results upon projection does not follow conventional rules of diagram theory and in fact in the normal state is a Z=0 non-Fermi liquid. Anomalous properties of this strange metal normal state are predicted and compared to experiments.

Abstract:
Based on a hybrid interlayer coupling mechanism, we study the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in trilayer cuprates. By introducing an interlayer magnetic scattering term, we solve the multilayer $t{-}J$ model with Josephson coupling under the framework of Gutzwiller projection. We show that both the SC and AFM orders in the multilayered system are enhanced and the range of AFM order is extended. The layer configuration of d-wave pairing gap and AFM order further plays an essential role in determining the interlayer magnetic and superconducting coupling phase diagram of such multilayered systems. Abrupt phase transitions between correlated states carrying distinct configurational symmetries are unveiled by tuning the doping level and/or the tunneling strengths.

Abstract:
The extended $t-J$ model is theoretically studied, in the context of hole underdoped cuprates. Based on results obtained by recent numerical studies, we identify the mean field state having both the antiferromagnetic and staggered flux resonating valence bond orders. The random-phase approximation is employed to analyze all the possible collective modes in this mean field state. In the static (Bardeen Cooper Schrieffer) limit justified in the weak coupling regime, we obtain the effective superconducting interaction between the doped holes at the small pockets located around $\bm{k}= (\pm \pi/2, \pm \pi/2)$. In contrast to the spin-bag theory, which takes into acccount only the antiferromagnetic order, this effective force is pair breaking for the pairing without the nodes in each of the small hole pocket, and is canceled out to be very small for the $d_{x^2-y^2}$ pairing with nodes which is realized in the real cuprates. Therefore we conclude that no superconducting instability can occur when only the magnetic mechanism is considered. The relations of our work with other approaches are also discussed.

Abstract:
We report systematic Cu- and F-NMR measurements of five-layered high-Tc cuprates Ba2Ca4Cu5O10(F,O)2. It is revealed that antiferromagnetism (AFM) uniformly coexists with superconductivity (SC) in underdoped regions, and that the critical hole density pc for AFM is ~ 0.11 in the five-layered compound. We present the layer-number dependence of AFM and SC phase diagrams in hole-doped cuprates, where pc for n-layered compounds, pc(n), increases from pc(1) ~ 0.02 in LSCO or pc(2) ~ 0.05 in YBCO to pc(5) ~ 0.11. The variation of pc(n) is attributed to interlayer magnetic coupling, which becomes stronger with increasing n. In addition, we focus on the ground-state phase diagram of CuO2 planes, where AFM metallic states in slightly doped Mott insulators change into the uniformly mixed phase of AFM and SC and into simple d-wave SC states. The maximum Tc exists just outside the quantum critical hole density, at which AFM moments on a CuO2 plane collapse at the ground state, indicating an intimate relationship between AFM and SC. These characteristics of the ground state are accounted for by the Mott physics based on the t-J model; the attractive interaction of high-Tc SC, which raises Tc as high as 160 K, is an in-plane superexchange interaction Jin (~ 0.12 eV), and the large Jin binds electrons of opposite spins between neighboring sites. It is the Coulomb repulsive interaction U ~ (> 6 eV) between Cu-3d electrons that plays a central role in the physics behind high-Tc phenomena.

Abstract:
In superconductors, electrons bound into Cooper pairs conduct a dissipationless current. The strength of the Cooper pairs scales with the value of the critical transition temperature (Tc). In cuprate high-Tc superconductors, however, the pairing mechanism is still unexplained. Here we unveil why in the cuprates the Cooper pairs are so strongly bound to work out the extraordinary high Tc. From one-to-one correspondence between numerical simulation on a microscopic cuprate model and a simple two-component fermion model, we show that hidden fermions emerge from the strong electron correlation and give birth to the strongly bound Cooper pairs. This mechanism is distinct from a conventional pairing mediated by some bosonic glue, such as phonons in conventional superconductors. The hidden fermions survive even above Tc and generate the strange-metal pseudogap phase. This reveals an unprecedented direct relationship between the pseudogap phase and superconductivity in the cuprates.

Abstract:
We review a recently proposed mechanism for superconductivity in hole-doped cuprates exhibiting a strong interplay between pairing and antiferromagnetism. Starting from the t-t'-J model for the CuO planes, we show that this interplay can explain in a unified framework the pseudogap phenomenology of the spectral weight of the hole, the hourglass-like structure of the magnetic excitation, the critical exponent of the superfluid density, the relation between the scale of the magnetic resonance and Tc.

Abstract:
When combining the BCS expression of Tc with a shear modulus constant model, we can demonstrate that Tc oscillates depending on the number of the cuprate planes and that it reaches its first maximum for three planes. This is in good agreement with experimental data and suggests that the electron- phonon coupling is essential to the superconductivity of the cuprates.

Abstract:
Local antiferromagnetism coexists with superconductivity in the cuprates. Charge segregation provides a way to reconcile these properties. Direct evidence for modulated spin and charge densities has been found in neutron and X-ray scattering studies of Nd-doped La(2-x)Sr(x)CuO(4). Here we discuss the nature of the modulation, and present some new results for a Zn-doped sample. Some of the open questions concerning the connections between segregation and superconductivity are described.