Abstract:
The anomalous features of the Raman spectroscopy measurement in MgB$_2$ represent a still unresolved puzzle. In particular highly debated are the origin of the huge $E_{2g}$ phonon linewidth, the nature of the low energy ($\omega < \omega_{E_{2g}}$) background and the evolution of the Raman spectra with Al doping. In this paper we compute the self-energy of the $E_{2g}$ phonon mode in a fully self-consistent way taking into account electron-phonon effects on the electronic properties. We show that all the anomalous features can be naturally understood in a framework where the whole electron-phonon spectrum $\alpha^2F(\omega)$ gives rise to significant damping processes for the electronic excitations and consequently for the $E_{2g}$ phonon itself. The two-peak structure as function of the Al doping is ascribed to finite bandwidth effects arising as the Fermi level approaches the $\sigma$ band edge.

Abstract:
We consider a model Hamiltonian fitted on the ab-initio band structure to describe the electron-phonon coupling between the electronic $\sigma-$bands and the phonon E$_{2g}$ mode in MgB$_2$. The model allows for analytical calculations and numerical treatments using very large k-point grids. We calculate the phonon self-energy of the E$_{2g}$ mode along two high symmetry directions in the Brillouin zone. We demonstrate that the contribution of the $\sigma$ bands to the Raman linewidth of the E$_{2g}$ mode via the electron-phonon coupling is zero. As a consequence the large resonance seen in Raman experiments cannot be interpreted as originated from the $E_{2g}$ mode at $\Gamma$. We examine in details the effects of Fermi surface singularities in the phonon spectrum and linewidth and we determine the magnitude of finite temperature effects in the the phonon self-energy. From our findings we suggest several possible effects which might be responsible for the MgB$_2$ Raman spectra.

Abstract:
The effect of pressure on optical phonon frequencies of MgB$_2$ has been calculated using the frozen-phonon approach based on a pseudopotential method. Gr\"uneisen parameters of the harmonic mode frequencies are reported for the high-frequency zone-center $E_{2g}$ and $B_{1g}$ and the zone-boundary $E_{2u}$ and $B_{2u}$ modes at $A$. Anharmonic effects of phonon frequencies and the implications of the calculated phonon frequency shifts for the pressure dependence of the superconducting transition temperature of MgB$_2$ are discussed. Also reported are Raman and optical reflectance spectra of MgB$_2$ measured at high pressures. The experimental observations in combination with calculated results indicate that broad spectral features we observed in the Raman spectra at frequencies between 500 and 900 cm$^{-1}$ cannot be attributed to first-order scattering by zone-center modes, but originate in part from a chemical species other than MgB$_2$ at the sample surface and in part from a maximum in the MgB$_2$ phonon density of states. Low-temperature Raman spectra taken at ambient pressure showed increased scattering intensity in the region below 300 cm$^{-1}$.

Abstract:
Room temperature Raman scattering measurements have been carried out on well characterized samples of MgB2-xCx. The Raman line corresponding to the E2g phonon mode shows progressive hardening from 620 cm-1 in pristine MgB2 to 775 cm-1 in the sample with carbon fraction x=0.2. The corresponding line width on the other hand, increases from a value of about 220 cm-1 to 286 cm-1 in samples with x = 0.1, beyond which it decreases to a value 167 cm-1 for x=0.2. From the average mode frequency and the line width obtained from Raman measurements and taking the values of N(0) obtained from the calculated variation in s hole density of states in MgB2-xCx, the electron phonon coupling strength to the E2g phonon, l2g, is evaluated using Allen’s formula. This remains large for low C fraction, but shows rapid decrease for x > 0.10. Using this value of l2g appropriately weighted, TC is obtained from McMillan’s equation. These values are in good agreement with the experimentally measured TC variation in MgB2-xCx.

Abstract:
We report tunneling measurements of the electron-phonon (e-ph) interaction in superconducting MgB$_2$ using the MgB$_2$-I-Nb junctions, where I stands for insulator. The phonon structure in tunneling density of states in MgB$_2$ clearly indicates strong e-ph coupling for the E$_{2g}$ in-plane boron phonons in a narrow range around 60 meV. The Eliashberg spectral function $\alpha^2(\omega)F(\omega)$ reconstructed from the tunneling data, exhibits significant additional contribution into e-ph interaction from other vibrations such as acoustic ($\sim 38$ meV) and optical ($\sim 90$ meV) bands. Our results are in reasonable agreement with neutron scattering experiments, and also to some data of Raman and infrared spectroscopy.

Abstract:
We report indications of a phase transition in carbonaceous MgB2 above 9 GPa at 300 K after stress relaxation by laser heating. The transition was detected using Raman spectroscopy and X-ray diffraction. The observed changes are consistent with a second-order structural transition involving a doubling of the unit cell along c and a reduction of the boron site symmetry. Moreover, the Raman spectra suggest a reduction in electron-phonon coupling in the slightly modified MgB2 structure consistent with the previously proposed topological transition in MgB2. However, further attributes including deviatoric stress, lattice defects, and compositional variation may play an important role in the observed phenomena.

Abstract:
Polarized Raman scattering measurements have been performed on Na0.5CoO2 single crystal from 8 to 305 K. Both the A1g and E1g phonon modes show a softening below Tc1 ~ 83 K. Additionally, the A1g phonon mode, which is forbidden in the scattering geometry of cross polarization for the triangular CoO2 layers, appears below Tc1. In contrast, the metal-insulator transition at Tc2 ~ 46 K has only secondary effect on the Raman spectra. The phonon softening and the ``forbidden'' Raman intensity follow closely magnetic order parameter and the gap function at the Fermi surface, indicating that the distortion of CoO6 octahedra at Tc1, instead of the Na ordering at ~350 K, is the relevant structural component of the 83 K phase transition.

Abstract:
We report the existence of broad and weakly asymmetric features in the high-energy (G) Raman modes of freely suspended metallic carbon nanotubes of defined chiral index. A significant variation in peak width (from 12 cm-1 to 110 cm-1) is observed as a function of the nanotube's chiral structure. When the nanotubes are electrostatically gated, the peak widths decrease. The broadness of the Raman features is understood as the consequence of coupling of the phonon to electron-hole pairs, the strength of which varies with the nanotube chiral index and the position of the Fermi energy.

Abstract:
The paper presents detailed Raman scattering study of the unusually broad E2g phonon mode in MgB2 crystal. For the first time, it is shown by the polarized Raman scattering on few-micron-size crystallites with natural faces that the observed broad Raman feature really does obey the selection rules of an E2g mode. Raman spectra on high quality polycrystalline superconducting MgB2 wires reveal a very symmetric E2g phonon line near 615 1/cm with the room temperature linewidth of 260 1/cm only. Additional scattering of different polarization dependence, observed in certain crystallites is interpreted as weighted phonon density of states induced by lattice imperfections.