Symmetry dependence of phonon lineshapes in superconductors with anisotropic gaps

The temperature dependence below $T_{c}$ of the lineshape of optical phonons of different symmetry as seen in Raman scattering is investigated for superconductors with anisotropic energy gaps. It is shown that the symmetry of the electron-phonon vertex produces non-trivial couplings to an anisotropic energy gap which leads to unique changes in the phonon lineshape for phonons of different symmetry. The phonon lineshape is calculated in detail for $B_{1g}$ and $A_{1g}$ phonons in a superconductor with $d_{x^{2}-y^{2}}$ pairing symmetry. The role of satellite peaks generated by the electron-phonon coupling are also addressed. The theory accounts for the substantial phonon narrowing of the $B_{1g}$ phonon, while narrowing of the $A_{1g}$ phonon which is indistinguishable from the normal state is shown, in agreement with recent measurements on BSCCO.Comment: 15 pages (3 Figures available upon request), Revtex, 1

Universal zero-frequency Raman slope in a d-wave superconductor

It is known that for an unconventional superconductor with nodes in the gap, the in-plane microwave or dc conductivity saturates at low temperatures to a universal value independent of the impurity concentration. We demonstrate that a similar feature can be accessed using channel-dependent Raman scattering. It is found that, for a $d_{x^2-y^2}$-wave superconductor, the slope of low-temperature Raman intensity at zero frequency is universal in the $A_{1g}$ and $B_{2g}$ channels, but not in the $B_{1g}$ channel. Moreover, as opposed to the microwave conductivity, universal Raman slopes are sensitive not only to the existence of a node, but also to different pairing states and should allow one to distinguish between such pairing states.Comment: 5 page

Momentum dependent light scattering in insulating cuprates

We investigate the problem of inelastic x-ray scattering in the spin$-{1/2}$ Heisenberg model on the square lattice. We first derive a momentum dependent scattering operator for the $A_{1g}$ and $B_{1g}$ polarization geometries. On the basis of a spin-wave analysis, including magnon-magnon interactions and exact-diagonalizations, we determine the qualitative shape of the spectra. We argue that our results may be relevant to help interpret inelastic x-ray scattering experiments in the antiferromagnetic phase of the cuprates.Comment: 5 pages, 3 figures, to appear in PR

Two Distinct Electronic Contributions in the Fully Symmetric Raman Response of High TcT_{c} Cuprates

We show by non resonant effect in HgBa$_2$CuO$_{4+\delta}$ (Hg-1201)and by Zn substitutions in YBa$_2$Cu$_3$O$_{7-\delta}$ (Y-123) compounds that the fully symmetric Raman spectrum has two distinct electronic contributions. The A$_{1g}$ response consists in the superconducting pair breaking peak at the 2$\Delta$ energy and a collective mode close to the magnetic resonance energy. These experimental results reconcile the \textit{d-wave} model to the A$_{1g}$ Raman response function in so far as a collective mode that is distinct from the pair breaking peak is present in the A$_{1g}$ channel.Comment: 4 pages, 2 figure

Resonant Enhancement of Inelastic Light Scattering in Strongly Correlated Materials

We use dynamical mean field theory to find an exact solution for inelastic light scattering in strongly correlated materials such as those near a quantum-critical metal-insulator transition. We evaluate the results for $\textbf{q}=0$ (Raman) scattering and find that resonant effects can be quite large, and yield a triple resonance, a significant enhancement of nonresonant scattering peaks, a joint resonance of both peaks when the incident photon frequency is on the order of $U$, and the appearance of an isosbestic point in all symmetry channels for an intermediate range of incident photon frequencies.Comment: 5 pages RevTex, 4 Figures ep

Optical sum rules that relate to the potential energy of strongly correlated systems

A class of sum rules for inelastic light scattering is developed. We show that the first moment of the non-resonant response provides information about the potential energy in strongly correlated systems. The polarization dependence of the sum rules provide information about the electronic excitations in different regions of the Brillouin zone. We determine the sum rule for the Falicov-Kimball model, which possesses a metal-insulator transition, and compare our results to the light scattering experiments in SmB_6.Comment: (5 pages, 3 figures, typeset in ReVTeX