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For half a century after the discovery of superconductivity, materials exploration for better superconductors proceeded without knowledge of the underlying mechanism. The 1957 BCS theory cleared that up: the superconducting state occurs due…
The 2014-2015 prediction, discovery, and confirmation of record high temperature superconductivity above 200K in H$_3$S, followed by the 2018 extension to superconductivity in the 250-280K range in lanthanum hydride, marks a new era in the…
This article is a review o over theory of superconductivity, which is constructed for systems with two overlapping energy bands at the Fermi surface and with arbitrary charge carrier density.There is taken into account all possible kinds of…
In several unconventional superconductors, the highest superconducting transition temperature $T_{c}$ is found in a region of the phase diagram where the antiferromagnetic transition temperature extrapolates to zero, signaling a putative…
When interacting electrons are confined to low-dimensions, the electron-electron correlation effect is enhanced dramatically, which often drives the system into exhibiting behaviors that are otherwise highly improbable. Superconductivity…
Achieving superconductivity at room temperature (RT) is a holy grail in physics. Recent discoveries on high-Tc superconductivity in binary hydrides H3S and LaH10 at high pressure have directed the search for RT superconductors to compress…
Models for strongly interacting fermions in disordered clusters forming an array, with electron hopping between sites, reproduce the linear dependence on temperature of the resistivity, typical of the strange metal phase of High Temperature…
Recently, superconductivity was discovered at very low densities in slightly misaligned graphene multilayers. Surprisingly, despite extremely low electronic density (about $10^{-4}$ electrons per unit cell), these systems realize…
Recently, the discovery of room-temperature superconductivity (SC) was experimentally realized in the fcc phase of LaH$_{10}$ under megabar pressures. This SC of compressed LaH$_{10}$ has been explained in terms of strong electron-phonon…
The spin-singlet superconductivity without phonons is examined in consideration of correlations on an extended Hubbard model. It is shown that the superconductivity requires not only the total correlation should be strong enough but also…
We consider possible high temperature superconductivity (high-T$_c$) in transition metal compounds with a cubic zinc-blende lattice structure. When the electron filling configuration in the d-shell is close to d$^7$, all three t$_{2g}$…
The search for room-temperature superconducting materials has been at the center of modern research for decades. The recent discovery of high-temperature superconductivity, under extreme pressure in hydrogen-rich materials, is a tremendous…
A systematic study of optical and transport properties of the Hubbard model, based on Metzner and Vollhardt's dynamical mean-field approximation, is reviewed. This model shows interesting anomalous properties that are, in our opinion,…
Self-assembling organic polymers and copper-oxide compounds are two classes of "strange" superconductors, whose challenging behavior does not comply with the traditional picture of Bardeen, Cooper, and Schrieffer (BCS) superconductivity in…
In this review article we consider theoretically and give experimental support to the models of the Fermi-Bose mixtures and the BCS-BEC crossover compared with the strong-coupling approach, which can serve as the cornerstones on the way…
Hydrogen in metals has attracted much attention for a long time from both basic scientific and technological points of view. Its electronic state has been investigated in terms of a proton embedded in the electron gas mostly by the local…
A theory of Kondo lattices is applied to the crossover between local-moment magnetism and itinerant-electron magnetism in the t-J model on a quasi-two dimensional lattice. The Kondo temperature T_K is defined as a characteristic temperature…
A comprehensive theory of superconductivity (SC) and superfluidity (SF) is presented of new types III and IV at temperatures into millions of degrees involving phase transitions of fermions in heat reservoirs to form general relativistic…
A two-band Hubbard model is used to describe the band structure and phase separation (PS) in multiband superconductors, especially in cuprates. We predict a large peak in the density of states at the Fermi level in the case of optimum…
It is well established that a correlated quantum impurity embedded in a metallic host can form the many-body Kondo state with itinerant electrons due to the effective antiferromagnetic coupling. Such effect is manifested spectroscopically…