Raman Scattering in Cuprate Superconductors

A theory for electronic Raman scattering in the cuprate superconductors is presented with a specific emphasis on the polarization dependence of the spectra which can infer the symmetry of the energy gap. Signatures of the effects of disorder on the low frequency and low temperature behavior of the Raman spectra for different symmetry channels provide detailed information about the magnitude and the phase of the energy gap. Properties of the theory for finite T are discussed and compared to recent data concerning the doping dependence of the Raman spectra in cuprate superconductors, and remaining questions are addressed.Comment: 27 pages, 11 figures, style file include

Collective Spin Fluctuation Mode and Raman Scattering in Superconducting Cuprates

Although the low frequency electronic Raman response in the superconducting state of the cuprates can be largely understood in terms of a d-wave energy gap, a long standing problem has been an explanation for the spectra observed in the $A_{1g}$ polarization orientations. We present calculations which suggest that the peak position of the observed $A_{1g}$ spectra is due to a collective spin fluctuation mode.Comment: 4 pages, 5 eps figure

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

Electronic Raman response in anisotropic metals

Using a generalized response theory we derive the electronic Raman response function for metals with anisotropic relaxation rates. The calculations account for the long--range Coulomb interaction and treat the collision operator within a charge conserving relaxation time approximation. We extend earlier treatments to finite wavenumbers ($|{\bf q}|\ll k_{\rm F}$) and incorporate inelastic electron--electron scattering besides elastic impurity scattering. Moreover we generalize the Lindhard density response function to the Raman case. Numerical results for the quasiparticle scattering rate and the Raman response function for cuprate superconductors are presented.Comment: 5 pages, 4figures. accepted in PRB (Brief Report), in pres

Quasiparticle interference and the interplay between superconductivity and density wave order in the cuprates

Scanning tunneling spectroscopy (STS) is a useful probe for studying the cuprates in the superconducting and pseudogap states. Here we present a theoretical study of the Z-map, defined as the ratio of the local density of states at positive and negative bias energies, which frequently is used to analyze STS data. We show how the evolution of the quasiparticle interference peaks in the Fourier transform Z-map can be understood by considering different types of impurity scatterers, as well as particle-hole asymmetry in the underlying bandstructure. We also explore the effects of density wave orders, and show that the Fourier transform Z-map may be used to both detect and distinguish between them.Comment: final version published in Phys. Rev.

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

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

Neutron Scattering and the B_{1g} Phonon in the Cuprates

The momentum dependent lineshape of the out-of-phase oxygen vibration as measured in recent neutron scattering measurements is investigated. Starting from a microscopic coupling of the phonon vibration to a local crystal field, the phonon lineshift and broadening is calculated as a function of transfered momentum in the superconducting state of YBa$_{2}$Cu$_{3}$O$_{7}$. It is shown that the anisotropy of the density of states, superconducting energy gap, and the electron-phonon coupling are all crucial in order to explain these experiments.Comment: new figures and discussio