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In the 35 years since the discovery of cuprate superconductors, we have not yet reached a unified understanding of their properties, including their material dependence of the superconducting transition temperature $T_{\text{c}}$. The…
Theoretical ideas and experimental results concerning high temperature superconductors are reviewed. Special emphasis is given to calculations carried out with the help of computers applied to models of strongly correlated electrons…
A brief history is offered concerning the relation of magnetism to superconductivity, and the possibility that magnetic correlations are responsible for certain types of superconductors. A central focus is on high temperature cuprate…
A profound problem in modern condensed matter physics is discovering and understanding the nature of the fluctuations and their coupling to fermions in cuprates which lead to high temperature superconductivity and the invariably associated…
Electron correlation effects are particularly strong in the high temperature superconducting materials. Devising an accurate description of these materials has long been a challenge, with these strong correlation effects historically being…
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…
High temperature superconductivity in the cuprates remains one of the most widely investigated, constantly surprising, and poorly understood phenomena in physics. Here, we describe briefly a new phenomenological theory inspired by the…
We deal with a model for high-temperature superconductivity which maintains that in cuprates electrons running in the copper oxide layers, found in lattice of these materials, form spin-singlet bonds with electrons running in the…
Current theoretical studies of electronic correlations in transition metal oxides typically only account for the local repulsion between d-electrons even if oxygen ligand p-states are an explicit part of the effective Hamiltonian.…
Superconductivity is an emergent phenomena in the sense that the energy scale associated with Cooper pairing is generically much lower than the typical kinetic energy of electrons. Addressing the mechanism of Cooper pairing amounts to…
We discuss the high-temperature superconductivity in copper oxide ceramics. We propose an effective Hamiltonian to describe the dynamics of electrons or holes injected into the copper oxide layers. We show that our approach is able to…
We deal with a model for high-temperature superconductivity which maintains that in cuprates spin-singlet bonds are formed between electrons running in the neighbouring layers of copper oxide found in lattice of these materials. This model…
Cuprates, ferropnictides and ferrochalcogenides are three classes of unconventional high-temperature superconductors, who share similar phase diagrams in which superconductivity develops after a magnetic order is suppressed, suggesting a…
High-temperature superconductors are nowadays found in great variety and hold technological promise. It is still an unsolved mystery that the critical temperature T_c of the basic cuprates is so high. The answer might well be hidden in a…
Developing a theory of high-temperature superconductivity in copper oxides is one of the outstanding problems in physics. It is a challenge that has defeated theoretical physicists for more than twenty years. Attempts to understand this…
We explore multiband effects on d-wave superconducting instabilities driven by electron-electron interactions. Our models on the two-dimensional square lattice consist of a main band with an extended Fermi surface and predominant weight…
The elementary CuO2 plane sustaining cuprate high-temperature superconductivity occurs typically at the base of a periodic array of edge-sharing CuO5 pyramids. Virtual transitions of electrons between adjacent planar Cu and O atoms,…
Understanding the complex phase diagram of cuprate superconductors is a long-standing challenging problem. Recent studies have shown that orbital degrees of freedom, both Cu $e_g$ orbitals and O $p$ orbitals, are a key ingredient for a…
The transition mechanism in high temperature cuprate superconductors is an outstanding puzzle. A previous suggestion on the role of non-linear local lattice instability modes on the microscopic pairing mechanism in high temperature cuprate…
A strategy to enhance d-wave superconducting correlations is proposed based on our numerical study for correlated electron models for high-Tc cuprates. We observe that the pairing is enhanced when the single-electron level around (pi,0) is…