Effect of electron-phonon interaction on the shift and attenuation of optical phonons

Using the Boltzmann equation for electrons in metals, we show that the optical phonons soften and have a dispersion due to screening in agreement with the results reported recently [M. Reizer, Phys. Rev. B {\bf 61}, 40 (2000)]. Additional phonon damping and frequency shift arise when the electron--phonon interaction is properly included.Comment: 4 pages, late

The Upper Critical Field Hc2 in Advanced Superconductors with Anisotropic Energy Spectrum

A brief review of works on the microscopic theory of determining the upper critical field in two-band isotropic and anisotropic superconductors is given. The research is based on a set of the Ginzburg-Landau equations for the order parameters in a magnetic field that are studied in terms of the classical approach to a superconducting system in a magnetic field. Two inequivalent energy bands with different topology of Fermi surface cavities overlapping on the Fermi surface are discussed. The cases of the direction of the external magnetic field H\to// the (ab) plane and H\to // the crystallographic c axis are studied. The equations for determining Hc2(ab) and Hc2(c) for a pure superconductor and a superconductor doped with electrons and holes are derived. The analytical solutions to these equations in the vicinity of the superconducting transition temperature (Tc - T<<Tc) and in the vicinity of zero (T<<Tc) are found. The temperature and impurity dependences of the upper critical fields Hc2(ab) and Hc2(c), as well as the anisotropy coefficient \gammaH, are studied. The resulting theory is applied to determine the dependences of the above magnetic characteristics of intermetallic compound MgB2. The theory agrees qualitatively with experimental data.Comment: 24 pages, 6 fi

Electronic Collective Modes and Superconductivity in Layered Conductors

A distinctive feature of layered conductors is the presence of low-energy electronic collective modes of the conduction electrons. This affects the dynamic screening properties of the Coulomb interaction in a layered material. We study the consequences of the existence of these collective modes for superconductivity. General equations for the superconducting order parameter are derived within the strong-coupling phonon-plasmon scheme that account for the screened Coulomb interaction. Specifically, we calculate the superconducting critical temperature Tc taking into account the full temperature, frequency and wave-vector dependence of the dielectric function. We show that low-energy plasmons may contribute constructively to superconductivity. Three classes of layered superconductors are discussed within our model: metal-intercalated halide nitrides, layered organic materials and high-Tc oxides. In particular, we demonstrate that the plasmon contribution (electronic mechanism) is dominant in the first class of layered materials. The theory shows that the description of so-called ``quasi-two-dimensional superconductors'' cannot be reduced to a purely 2D model, as commonly assumed. While the transport properties are strongly anisotropic, it remains essential to take into account the screened interlayer Coulomb interaction to describe the superconducting state of layered materials.Comment: Final version (minor changes) 14 pages, 6 figure

Specific Heat Discontinuity in Impure Two-Band Superconductors

The Ginzburg-Landau coefficients, and the jump of the specific heat are calculated for a disordered two-band superconductor. We start with the analysis of a more general case arbitrary anisotropy. While the specific heat discontinuity at the critical temperature T_c decreases with increasing disorder, its ratio to the normal state specific heat at T_c increases and slowly converges to the isotropic value. For a strong disorder the deviation from the isotropic value is proportional to the elastic electron scattering time. In the case of a two-band superconductor we apply a simplified model of the interaction independent on momentum within a band. In the framework of this model all thermodynamic values can be found explicitly at any value of the scattering rate. This solution explains the sample dependence of the specific heat discontinuity in MgB_2 and the influence of the disorder on the critical temperature.Comment: New results relate to two-band superconductors, 9 pages, 2 figure

Ginzburg-Landau theory of vortices in a multi-gap superconductor

The Ginzburg-Landau functional for a two-gap superconductor is derived within the weak-coupling BCS model. The two-gap Ginzburg-Landau theory is, then, applied to investigate various magnetic properties of MgB2 including an upturn temperature dependence of the transverse upper critical field and a core structure of an isolated vortex. Orientation of vortex lattice relative to crystallographic axes is studied for magnetic fields parallel to the c-axis. A peculiar 30-degree rotation of the vortex lattice with increasing strength of an applied field observed by neutron scattering is attributed to the multi-gap nature of superconductivity in MgB2.Comment: 11 page

Challenging the nature of low-energy plasmon excitations in CaC 6

The nature of low energy plasmon excitations plays an important role in understanding the low energy electronic properties and coupling mechanism of different superconducting compounds such as CaC$_6$. Recent ab-initio studies predict a charge carrier intraband plasmon in keeping with a low energy acoustic plasmon. Here, we have studied the low-energy electronic excitations of CaC$_6$ using high-resolution electron energy-loss spectroscopy in transmission at low temperatures. The analysis of the core-level excitations leads to the conclusion that hybridization between graphite and calcium states plays an essential role in this graphite intercalated compound. Regarding the low energy plasmon excitation, we observe the formation of an intraband (charge carrier) plasmon with a negative dispersion at about 3.5 eV in sound agreement with the theory. Finally, a weak excitation around 1.2 eV with an almost linear dispersion relation can be observed as predicted for an acoustic plasmon that may mediate the superconducting coupling in CaC$_6$. However its optical limit at ~1 eV challenges the theoretical predictions and safely rules out an electronic superconducting coupling mechanism in CaC$_6$.Comment: 5 figure