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It is argued that the BCS many-body theory, which is outstandingly successful for conventional superconductors, does not apply to the high temperature superconductors and that a realistic theory must take account of the local electronic…
The interplay between the band Jahn-Teller distortion and the superconductivity is studied for the system whose Fermi level lies in two-fold degenerate band. Assuming that the lattice distortion is coupled to the orbital electron density…
The type I superconductor lead (Pb) has been theoretically predicted to be a two-band superconductor. We use scanning tunneling spectroscopy (STS) to resolve two superconducting gaps with an energy difference of 150$\,\mu$eV. Tunneling into…
The discovery of high-$T_c$ superconductivity in the pnictides, materials with a Fermi surface determined by several bands, highlights the need to understand how superconductivity arises in multiband systems. In this effort, using symmetry…
We develop the Bardeen-Cooper-Schrieffer (BCS) formalism for the superconductivity of carbon nanotubes. It is found that the superconducting transition temperature Tc of single-wall carbon nanotubes decreases exponentially with the increase…
The BCS picture of superconductivity describes pairing between electrons originating from a single band. A generalization of this picture occurs in multi-band superconductors, where electrons from two or more bands contribute to…
We consider the far-infrared and the microwave conductivities of a two-band superconductor with non-magnetic impurities. The strong coupling expressions for the frequency and temperature dependent conductivity of a two-band superconductor…
The calculations of the local and global properties of two band superconductors have been presented with particular attention to the role of the inter-orbital scattering of pairs. The properties of such superconductors are very different…
The proximity effect refers to the phenomenon whereby superconducting properties are induced in a normal conductor that is in contact with an intrinsically superconducting material. In particular, the combination of nano-structured…
We present a combined experimental and theoretical study of the proximity effect in an atomic-scale controlled junction between two different superconductors. Elaborated on a Si(111) surface, the junction comprises a Pb nanocrystal with an…
Superconductivity has been observed in doped SrTiO$_3$ at charge-carrier densities below 10$^{18}$ cm$^{-3}$, where the density of states at the Fermi level of the itinerant electrons is several orders of magnitude lower than that of…
We examine possibility of enhancement of superconductive critical temperature in two-dimensions. The weak coupling BCS theory is applied, especially when the Fermi level is near the edges of the electronic bands. The attractive interaction…
A combination of strong Cooper pairing and weak superconducting fluctuations is crucial to achieve and stabilize high-Tc superconductivity. We demonstrate that a coexistence of a shallow carrier band with strong pairing and a deep band with…
The basic features of multi-band superconductivity and its implications are derived. In particular, it is shown that enhancements of the superconducting transition temperature take place due to interband interactions. In addition, isotope…
We consider a multiband metal with deep primary bands and a shallow secondary one. In the normal state the system undergoes Lifshitz transition when the bottom of the shallow band crosses the Fermi level. In the superconducting state Cooper…
We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. The Fermi-Dirac…
The power-law temperature dependences of the specific heat, the nuclear relaxation rate, and the thermal conductivity suggest the presence of line nodes in the superconducting gap of Sr2RuO4. These recent experimental observations…
We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk "poor conductors" in which Fermi energy $E_F$ is located in the region of localized states not so far from the Anderson mobility edge $E_c$.…
Superconductivity (SC) may microscopically coexist with density wave (DW) when the nesting of the Fermi surface (FS) is not perfect. There are, at least, two possible microscopic structures of a DW state with quasi-particle states remaining…
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…