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Recent experiments on certain Fe-based superconductors have hinted at a role for paired electrons in "incipient" bands that are close to, but do not cross the Fermi level. Related theoretical works disagree on whether or not strong-coupling…
A theory of Kondo lattices or a $1/d$ expansion theory, with $d$ spatial dimensionality, is applied to studying itinerant-electron ferromagnetism. Two relevant multi-band models are examined: a band-edge model where the chemical potential…
Superconductivity has again become a challenge following the discovery of unconventional superconductivity. Resistance-free currents have been observed in heavy-fermion materials, organic conductors and copper oxides. The discovery of…
We develop a theory of a pseudogap state appearing near the superconductor-insulator transition in strongly disordered metals with attractive interaction. We show that such an interaction combined with the fractal nature of the single…
I present a theory of electron dynamics in semiconductors with slowly varying composition. I show that the frequency-dependent conductivity, required for the description of transport and optical properties, can be obtained from a knowledge…
One of the central questions about the iron pnictides concerns the extent to which their electrons are strongly correlated. Here we address this issue through the phenomenology of the charge transport and dynamics, single-electron…
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…
We theoretically describe a mechanism of low-field linear magnetoconductivity in helical magnetic metals. Two ingredients for the mechanism in three-dimensional metals are identified to be the spin-orbit coupling and momentum-dependent…
High-transition temperature (high-$T_c$) superconductivity in the iron pnictides/chalcogenides emerges from the suppression of the static antiferromagnetic order in their parent compounds, similar to copper oxides superconductors. This…
The phenomenon of flat bands pinned to the Fermi surface is analyzed on the basis of the Landau-Pitaevskii relation, which is applicable to electron systems of solids. It is shown that the gross properties of normal states of high-$T_c$…
Two-dimensional moire superlattices have recently emerged as a fertile ground for creating novel electronic phases of matter with unprecedented control. Despite intensive efforts, theoretical investigation of correlated moire systems has…
In this review, the authors present a summary of experimental reports on newly discovered iron-based superconductors as they were known at the end of 2008. At the same time, this paper is intended to be useful for experimenters to know the…
The apparently inimical relationship between magnetism and superconductivity has come under increasing scrutiny in a wide range of material classes, where the free energy landscape conspires to bring them in close proximity to each other.…
We present a general thermodynamic theory that describes phases and phase transitions of ferromagnetic superconductors with spin-triplet electron Cooper pairing. The theory is based on extended Ginzburg-Landau expansion in powers of…
We consider phase transitions and potential co-existence of spin-density-wave (SDW) magnetic order and extended s-wave ($s^+$) superconducting order within a two-band itinerant model of iron pnictides, in which SDW magnetism and $s^+$…
We present a two-fluid description for iron-based superconductors, which contains an itinerant electron Fermi-liquid and a local moment spin-liquid, coupled together via an effective Hund's rule interaction. We examine the low-energy…
Recent discovery of high T_c superconductivity in Fe-based compounds may have opened a new pathway to the room temperature superconductivity. The new materials feature FeAs layers instead of the signature CuO_2 planes of much-studied…
We suggest a new family of Co/Ni-based materials that may host unconventional high temperature superconductivity (high-T$_c$). These materials carry layered square lattices with each layer being formed by vertex-shared transition metal…
This paper is written as a brief introduction for beginning graduate students. The picture of electron waves moving in a cristalline potential and interacting weakly with each other and with cristalline vibrations suffices to explain the…
Electron correlations play a central role in iron-based superconductors. In these systems, multiple Fe $3d$-orbitals are active in the low-energy physics, and they are not all degenerate. For these reasons, the role of orbital-selective…