High Tc Superconductors -- A Variational Theory of the Superconducting State

We, basing on the quantum critical point (QCP)($p = 0.19 $), propose a phenomenological description on high-$T_c$ superconductivity in the cuprate superconductors, and suggest it divides the whole doping region into two parts: the underdoped region ($p < 0.19 $) and the overdoped region ($ p> 0.19 $). The electrons in the former are localized and form the localized Fermi liquid, a kind of the non-Fermi liquid, where the carriers are the holes; the electrons in the latter are ...

High temperature superconductivity encompasses the cuprates, nickelates, iron pnictides, and LaH$_x$ compounds. The first three groups of compounds involve in the pairing electrons, which are strongly to moderately correlated, whereas in the last class of systems specific phonon excitations. In this overview we concentrate first on the (semi)quantitative theory of high T$_{C}$ superconductivity in the cuprates based on our original vibrational approach beyond the renormalized...

In a recent review by Anderson and coworkers\cite{Vanilla}, it was pointed out that an early resonating valence bond (RVB) theory is able to explain a number of unusual properties of high temperature superconducting (SC) Cu-oxides. Here we extend previous calculations \cite{anderson87,FC Zhang,Randeria} to study more systematically low energy physical properties of the plain vanilla d-wave RVB state, and to compare results with the available experiments. We use a renormalized...

It has been now over 20 years since the discovery of the first high temperature superconductor by Georg Bednorz and Alex Mueller in 1986 and yet, despite intensive effort, no universally accepted theory exists about the origin of high-temperature superconductivity. A controversial issue on whether the electron-phonon interaction (EPI) is crucial for high-temperature superconductivity or weak and inessential has been one of the most challenging problems of contemporary condens...

We use a symmetry-constrained variational procedure to construct a generalization of BCS to include Cooper pairs with non-zero momentum and angular momentum. The resulting gap equations are solved at zero and finite temperature, and the doping-dependent solutions are used to construct gap and phase diagrams. We find a pseudogap terminating at a critical doping that may be interpreted in terms of both competing order and preformed pairs. The strong similarity between observati...

Superconductivity in cuprate superconductors occurs upon charge-carrier doping Mott insulators, where a central question is what mechanism causes the loss of electrical resistance below the superconducting (SC) transition temperature? In this review, we attempt to summarize the basic idea of the kinetic-energy driven SC mechanism in the description of superconductivity in cuprate superconductors. The mechanism of the kinetic-energy driven superconductivity is purely electroni...

We discuss recent progress of understanding the phenomena observed in high Tc cuprates by studying the d-wave resonating-valence-bond (d-RVB) based trial wave functions for the 2-dimensional t-J-type models. Treat exactly the strong correlation between electrons by numerical approach, we examine the evolution of ground states described by different variational wave functions and properties of the quasi-hole and -particle excitations of the d-RVB superconducting (SC) state. Pr...

Since their experimental discovery in 1989, the electron-doped cuprate superconductors have presented both a major challenge and a major opportunity. The major challenge has been to determine whether these materials are fundamentally different from or essentially similar to their hole-doped counterparts; a major opportunity because answering this question would strongly constrain the possible explanations for what is the essential physics that leads to high temperature superc...

The discovery of high temperature superconductivity in the cuprates in 1986 triggered a spectacular outpouring of creative and innovative scientific inquiry. Much has been learned over the ensuing 28 years about the novel forms of quantum matter that are exhibited in this strongly correlated electron system. This progress has been made possible by improvements in sample quality, coupled with the development and refinement of advanced experimental techniques. In part, avenues ...

Thermodynamic quantities are derived for superconducting and pseudogap regimes by taking into account both amplitude and phase fluctuations of the pairing field. In the normal (pseudogap) state of the underdoped cuprates, two domains have to be distinguished: near the superconducting region, phase correlations are important up to the temperature $T_\phi$. Above $T_\phi$, the pseudogap region is only determined by amplitudes, and phases are uncorrelated. Our calculations sho...