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We present a review of theoretical and experimental works on the problem of mutual interplay of Anderson localization and superconductivity in strongly disordered systems. We start with brief discussion of modern aspects of localization…
The color superconductivity of a dense quark matter is reviewed with emphasis on the long range nature of the pairing force and the multiplicity of the order parameter. The former gives rise to a non BCS behavior of the superconducting…
Unconventional superconductors represent one of the most intriguing quantum states of matter. In particular, multiorbital systems have the potential to host exotic non-unitary superconducting states. While the microscopic origin of…
Apparently conflicting phase-sensitive measurements of the order parameter symmetry in the high-T$_c$ superconductors may be explained by regions near surfaces in which the order parameter symmetry is different than in the bulk. These…
Although the microscopic origin of the superconductivity in high Tc copper oxides remains the subject of active inquiry, several of their electronic characteristics are well established as universal to all the known materials, forming the…
Experiments have observed superconductivity in atomically-thin metallic layers deposited on semiconducting substrates. As in any superconductor, it is important to determine the structure of the superconducting pairing function in order to…
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…
Effects of inhomogeneous doping on the high-$T_c$ cuprate superconductors are studied within the framework of the t-J model. Especially, the boundary between two non-superconducting regions with doping rates much higher and lower than the…
The surprising discovery of superconductivity in layered iron-based materials, with transition temperatures climbing as high as 55 K, has lead to thousands of publications on this subject over the past two years. While there is general…
We propose a finite temperature Landau theory that describes competing orders and interlayer tunneling in cuprate superconductors as an important extension to a corresponding theory at zero temperature [Nature {\bf 428}, 53 (2004)], where…
In high-transition temperature (high-Tc) copper oxides, it is generally believed that antiferromagnetism plays a fundamental role in the superconducting mechanism because superconductivity occurs when mobile electrons or holes are doped…
Two families of high temperature superconductors whose critical temperatures are higher than 50K are known. One is the copper oxides and the other is the iron-based superconductors. Comparisons of mechanisms between these two in terms of…
There have been several proposals for platforms sustaining topological superconductivity in high temperature superconductors, in order to make use of the larger superconducting gap and the expected robustness of Majorana zero modes towards…
We present new estimates on the two-dimensional Ginzburg-Landau energy of a type-II superconductor in an applied magnetic field varying between the second and third critical fields. In this regime, superconductivity is restricted to a thin…
Recent progress in two-dimensional superconductors with atomic-scale thicknesses is reviewed mainly from the experimental point of view. The superconducting systems treated here involve a variety of materials and forms: elemental-metal…
On the basis of coupled Ginzburg--Landau equations we study nonhomogeneous states in systems with two order parameters~(OP). Superconductors with superconducting OP~$\Delta$, and charge- or spin-density wave (CDW or SDW) with amplitude~$W$…
One of the leading issues in high-$\rm T_c$ copper oxide superconductors is the origin of the pseudogap phase in the underdoped regime of their phase diagram. Using polarized neutron diffraction, a novel magnetic order has been identified…
Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such…
The criticism of Babaev and Silaev notwithstanding, we conclude that our analysis is correct. We have found in our papers on two-band superconductors close to Tc, where the Ginzburg-Landau (GL) theory applies, that these materials are…
25 years after discovery of high-temperature superconductivity (HTSC) in La$_{2-x}$Ba$_x$CuO$_4$ (LBCO), the HTSC continues to pose some of the biggest challenges in materials science. Cuprates are fundamentally different from conventional…