Abstract:
Tunneling data on MgB_{1.8}C_{0.2} show a reduction in the energy gap of the pi-bands by a factor of two from undoped MgB2 that is consistent with the Tc reduction, but inconsistent with the expectations of the dirty limit. Dirty-limit theory for undoped MgB2 predicts a single gap about three times larger than measured and a reduced Tc comparable to that measured. Our heavily-doped samples exhibit a uniform dispersion of C suggestive of significantly enhanced scattering, and we conclude that the retention of two-band superconductivity in these samples is caused by a selective suppression of interband scattering.

Abstract:
The superconducting gap of MgB2 has been studied by high-resolution angle-resolved photoemission spectroscopy (ARPES). The momentum(k)-resolving capability of ARPES enables us to identify the s- and p-orbital derived bands predicted from band structure calculations and to successfully measure the superconducting gap on each band. The results show that superconducting gaps with values of 5.5 meV and 2.2 meV open on the s-band and the p-band, respectively, but both the gaps close at the bulk transition temperature, providing a definitive experimental evidence for the two-band superconductivity in MgB2. The experiments validate the role of k-dependent electron-phonon coupling as the origin of multiple-gap superconductivity in MgB2.

Abstract:
We report $^{11}$B-NMR study on Al-doped MgB$_2$ that addresses a possible mechanism for a high superconducting (SC) transition temperature ($T_c$) of $\sim 40$ K in recently discovered MgB$_2$. The result of nuclear spin lattice relaxation rate $1/T_1$ in the SC state revealed that the size in the SC gap is not changed by substituting Al for Mg. The reduction on $T_c$ by Al-doping is shown to be due to the decrease of $N(E_F)$. According to the McMillan equation, the experimental relation between $T_c$ and the relative change in $N(E_F)$ allowed us to estimate a characteristic phonon frequency $\omega \sim 700$ K and an electron-phonon coupling constant $\lambda \sim 0.87$. These results suggest that the high-$T_c$ superconductivity in MgB$_2$ is mediated by the strong electron-phonon coupling with high-frequency phonons.

Abstract:
It is shown that the superconducting intermetallic compound MgB2 possesses a narrow, partly filled "superconducting band" with Wannier functions of special symmetry in its band structure. This result corroborates previous observations about the band structures of numerous superconductors and non-superconductors showing that evidently superconductivity is always connected with such superconducting bands. These findings are interpreted in the framework of a nonadiabatic extension of the Heisenberg model. Within this new group-theoretical model of correlated systems, Cooper pairs are stabilized by a nonadiabatic mechanism of constraining forces effective in narrow superconducting bands. The formation of Cooper pairs in a superconducting band is mediated by the energetically lowest boson excitations in the considered material that carry the crystal spin-angular momentum 1 x h-bar. These crystal-spin-1 bosons are proposed to determine whether the material is a conventional low-Tc or a high-Tc superconductor. This interpretation provides the electron-phonon mechanism that enters the BCS theory in conventional superconductors.

Abstract:
The study of the anisotropic superconductor MgB2 using a combination of scanning tunneling microscopy and spectroscopy reveals two distinct energy gaps at Delta1=2.3 meV and Delta2=7.1 meV. Different spectral weights of the partial superconducting density of states (PDOS) are a reflection of different tunneling directions in this multi-band system. Our experimental observations are consistent with the existence of two-band superconductivity in the presence of interband superconducting pair interaction and quasiparticle scattering. Temperature evolution of the tunneling spectra follows the BCS scenario with both gaps vanishing at the bulk Tc. Indeed, the study of tunneling junctions exhibiting only the small gap (c-axis tunneling) clearly and reproducibly show that this gap persists up to the bulk Tc. The data confirm the importance of Fermi-surface sheet dependent superconductivity in MgB2 proposed in the multigap model by Liu et al.

Abstract:
The theory of thermodynamic properties of two-band superconductor with reduced density charge carriers is developed on the base of phonon superconducting mechanism with strong electron-phonon interaction. This theory is adapted to describe the behavior of critical temperature Tc, energy gaps Delta1, Delta2, and the relative jump of electron specific heat (Cs - Cn)/Cn in the point T = Tc along with the variation of charge carrier density in the compound MgB2 when substitutional impurities with different valence are introduced into the system. It is shown, that according to the filling mechanism of energy bands which overlap on Fermi surface, the quantities Tc, Delta1, Delta2 decrease when this compound is doped with electrons and remain constant or weakly change when the system is doped with holes. The theory qualitatively agrees with the experimental data. Also is shown that the consideration of inter- and intraband scattering of electrons on impurity potential improves this agreement.

Abstract:
The damaging effect of strong electron-electron repulsion on regular, electron-phonon %$s$-wave superconductivity is a standard tenet. In spite of that, an increasing number of compounds such as fullerides and more recently alkali-doped aromatics exhibit %$s$-wave or presumably $s$ wave superconductivity despite very narrow bands and very strong electron repulsion. Here, we explore superconducting solutions of a model Hamiltonian inspired by the electronic structure of alkali doped aromatics. The model is a two-site, two-narrow-band metal with a single intersite phonon, leading to attraction-mediated, two-order parameter superconductivity. On top of that, the model includes a repulsive on-site Hubbard $U$, whose effect on the superconductivity we study. Starting within mean field, we find that $s \pm$ superconductivity is the best solution surviving the presence of $U$, whose effect is canceled out by the opposite signs of the two order parameters. The correlated Gutzwiller study that follows is necessary because without electron correlations the superconducting state would in this model be superseded by an antiferromagnetic insulating state with lower energy. The Gutzwiller correlations lower the energy of the metallic state, with the consequence that the $s \pm$ superconducting state is stabilized and even strengthened for small Hubbard $U$.

Abstract:
Superconductivity of boron-doped diamond, reported recently at T_c=4 K, is investigated exploiting its electronic and vibrational analogies to MgB2. The deformation potential of the hole states arising from the C-C bond stretch mode is 60% larger than the corresponding quantity in MgB2 that drives its high Tc, leading to very large electron-phonon matrix elements. The calculated coupling strength \lambda ~ 0.5 leads to T_c in the 5-10 K range and makes phonon coupling the likely mechanism. Higher doping should increase T_c somewhat, but effects of three dimensionality primarily on the density of states keep doped diamond from having a T_c closer to that of MgB2.

Abstract:
We predict that electron-doped silicene is a good two-dimensional electron-phonon superconductor under biaxial tensile strain by first-principles calculations within rigid band approximation. Superconductivity transition temperature of electron-doped silicene can be increased to be above 10 K by 5% tensile strain. Band structures, phonon dispersive relations, and Eliashberg functions are calculated for detailed analysis. The strong interaction between acoustic phonon modes normal to the silicene plane and the increasing electronic states around the Fermi level induced by tensile strain is mainly responsible for the enhanced critical temperature.

Abstract:
In this work the effect of Carbon and Aluminium doping on the multiband MgB2 superconductor is analyzed. Using the rigid band and virtual crystal approximations (RBA and VCA), it was found that the main effect of doping on the band structure is band filling and a relative band-shift. If this band-shift is eliminated with an appropriate change of scale, then the RBA provides a good description of the band structure as function of doping. With this procedure both the inplane electrical conductivity of the C- and Al-doped MgB2 and the superconducting critical temperature follow the same curve. The Tc graph approximately follows the sigma-band density of states; the differences between these two can be explained by loss of anisotropy which plays an important role in these systems.