Impurity effects on optical response in a finite band electronic system coupled to phonons

The concepts, which have traditionally been useful in understanding the effects of the electron--phonon interaction in optical spectroscopy, are based on insights obtained within the infinite electronic band approximation and no longer apply in finite band metals. Impurity and phonon contributions to electron scattering are not additive and the apparent strength of the coupling to the phonon degrees of freedom is substantially reduced with increased elastic scattering. The optical mass renormalization changes sign with increasing frequency and the optical scattering rate never reaches its high frequency quasiparticle value which itself is also reduced below its infinite band value

Effect of disorder on the NMR relaxation rate in two-band superconductors

We calculate the effect of nonmagnetic impurity scattering on the spin-lattice relaxation rate in two-band superconductors with the s-wave pairing symmetry. It is found that for the interaction parameters appropriate for MgB2 the Hebel-Slichter peak is suppressed by disorder in the limit of small interband impurity scattering rate. In the limit of strong impurity scattering, when the gap functions in the two bands become nearly equal, the single-band behavior is recovered with a well-defined coherence peak just below the transition temperature.Comment: 6 pages, 4 figure

Finite band inversion of ARPES in Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta} in comparison with optics

Using a maximum entropy technique within a finite band Eliashberg formalism we extract from recent high accuracy nodal direction angular resolved photo-emission spectroscopy (ARPES) data in optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) a quasiparticle electron-boson spectral density. Both normal and superconducting state with d-wave gap symmetry are treated. Finite and infinite band results are considered and contrasted. We compare with results obtained for the related transport spectral density which follows from a similar inversion of optical data. We discuss the implication of our results for quasiparticle renormalizations in the antinodal direction.Comment: 9 pages, 7 figures submitted to Physical Review

Effect of electron-phonon interaction on spectroscopies in graphene

We calculate the effect of the electron-phonon interaction on the electronic density of states (DOS), the quasiparticle properties and on the optical conductivity of graphene. In metals with DOS constant on the scale of phonon energies, the electron-phonon renormalizations drop out of the dressed DOS, however, due to the Dirac nature of the electron dynamics in graphene, the band DOS is linear in energy and phonon structures remain, which can be emphasized by taking an energy derivative. There is a shift in the chemical potential and in the position in energy of the Dirac point. Also, the DOS can be changed from a linear dependence out of value zero at the Dirac point to quadratic out of a finite value. The optical scattering rate $1/\tau$ sets the energy scale for the rise of the optical conductivity from its universal DC value $4e^2/\pi h$ (expected in the simplest theory when chemical potential and temperature are both $\ll 1/2\tau$) to its universal AC background value $(\sigma_0=\pi e^2/2h)$. As in ordinary metals the DC conductivity remains unrenormalized while its AC value is changed. The optical spectral weight under the intraband Drude is reduced by a mass renormalization factor as is the effective scattering rate. Optical weight is transferred to an Holstein phonon-assisted side band. Due to Pauli blocking the interband transitions are sharply suppressed, but also nearly constant, below twice the value of renormalized chemical potential and also exhibit a phonon-assisted contribution. The universal background conductivity is reduced below $\sigma_0$ at large energies.Comment: 22 pages, 19 figures, submitted to PR

Classical phase fluctuations in d-wave superconductors

We study the effects of low-energy nodal quasiparticles on the classical phase fluctuations in a two-dimensional d-wave superconductor. The singularities of the phase-only action at T\to 0 are removed in the presence of disorder, which justifies using an extended classical XY-model to describe phase fluctuations at low temperatures.Comment: 14 pages, brief review for Mod. Phys. Lett.

Properties of the superconducting state in a two-band model

Eliashberg theory is used to investigate the range of thermodynamic properties possible within a two-band model for s-wave superconductivity and to identify signatures of its two-band nature. We emphasize dimensionless BCS ratios (those for the energy gaps, the specific heat jump and the negative of its slope near Tc, the thermodynamic critical field Hc(0), and the normalized slopes of the critical field and the penetration depth near Tc), which are no longer universal even in weak coupling. We also give results for temperature-dependent quantities, such as the penetration depth and the energy gap. Results are presented both for microscopic parameters appropriate to MgB2 and for variations away from these. Strong coupling corrections are identified and found to be significant. Analytic formulas are provided which show the role played by the anisotropy in coupling in some special limits. Particular emphasis is placed on small interband coupling and on the opposite limit of no diagonal coupling. The effect of impurity scattering is considered, particularly for the interband case.Comment: 20 pages, 14 figures, final version accepted in PR

Phonon spectroscopy through the electronic density of states in graphene

We study how phonon structure manifests itself in the electronic density of states of graphene. A procedure for extracting the value of the electron-phonon renormalization $\lambda$ is developed. In addition, we identify direct phonon structures. With increasing doping, these structures, along with $\lambda$, grow in amplitude and no longer display particle-hole symmetry.Comment: 5 page