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Preformed pairs above $T_c$ and the two-gap scenarios are two main proposals for describing the low doping pseudogap phase of high-$T_c$ cuprates. Very recent angle-resolved photoemission experiments have shown features which were…
The anomalous properties of High-$T_{{\rm c}}$ cuprates are investigated both in the normal state and in the superconducting state. In particular, we pay atte ntion to the pseudogap in the normal state and the phase transition from the pse…
The superconducting phase of the high-Tc cuprates has been thought to be described by a single d-wave pairing order parameter. Recently, there has been growing evidence suggesting that another form of order, possibly inherited from the…
It has become clear in the past several years that the cuprates show many unusual properties, both in the normal and superconducting states, especially in the underdoped region. In particular, gap-like behavior is observed in magnetic…
A pairing gap and coherence are the two hallmarks of superconductivity. In a classical BCS superconductor they are established simultaneously at Tc. In the cuprates, however, an energy gap (pseudogap) extends above Tc. The origin of this…
The pseudogap stands out in the phase diagram of the cuprate high-temperature superconductors because its origin and relationship to superconductivity remain elusive. The origin of the pseudogap has been debated, with competing hypotheses…
Understanding high-temperature superconductivity in cuprates requires knowledge of the metallic phase it evolves from, particularly the pseudogap profoundly affecting the electronic properties at low carrier densities. A key question is the…
One of the most intriguing aspects of cuprates is a large pseudogap coexisting with a high superconducting transition temperature. Here, we study pairing in the cuprates from electron-electron interactions by constructing the pair vertex…
The pseudogap phase of the underdoped cuprate superconductors harbours diverse manifestations of different ordered electronic-states, and then these ordered electronic-states coexist or compete with superconductivity. Here starting from the…
One of the most remarkable properties of the high-temperature superconductors is a pseudogap regime appearing in the underdoped cuprates above the superconducting transition temperature T_c. The pseudogap continously develops out of the…
A term first coined by Mott back in 1968 a `pseudogap' is the depletion of the electronic density of states at the Fermi level, and pseudogaps have been observed in many systems. However, since the discovery of the high temperature…
When the Mott insulating state is suppressed by charge carrier doping, the pseudogap phenomenon emerges, where at the low-temperature limit, superconductivity coexists with some ordered electronic states. Within the framework of the…
We report atomic scale characterization of the pseudogap state in a high-T$_c$ superconductor, Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. The electronic states at low energies within the pseudogap exhibit spatial modulations having an…
One of the puzzling characteristics of the pseudogap phase of high-$T_c$ cuprates is the nodal-antinodal dichotomy. While the nodal quasiparticles have a Fermi liquid behaviour, the antinodal ones show non-Fermi liquid features and an…
We describe the spectral properties of underdoped cuprates as resulting from a momentum-dependent pseudogap in the normal state spectrum. Such a model accounts, within a BCS approach, for the doping dependence of the critical temperature…
The t-J model is a paradigmatic model for the study of strongly correlated electron systems. In particular, it has been argued that it is an appropriate model to describe the cuprate high-Tc superconductors. It turns out that a…
In the last few years evidence has been accumulating that there are a multiplicity of energy scales which characterize superconductivity in the underdoped cuprates. In contrast to the situation in BCS superconductors, the phase coherence…
Relationship between the superconducting gap and the pseudogap has been the subject of controversies. In order to clarify this issue, we have studied the superconducting gap and pseudogap of the high-Tc superconductor La2-xSrxCuO4 (x=0.10,…
The microscopic origin of the pseudogap state which exists in the underdoped cuprates remains unknown. The $c$-axis properties in the pseudogap regime are particularly anomalous. We use a recently proposed model of a $d$-density wave which…
I begin by briefly reviewing various experimental results on the pseudogap phenomena in underdoped cuprates. I argue that, taken together, all of these lead to a picture of singlet pairing above $T_c$. I then explore the idea that the…