Optical sum rule in metals with a strong interaction

The restricted optical sum rule and its dependence on the temperature, a superconducting gap and the cutoff energy have been investigated. As known this sum rule depends on the cutoff energy and the relaxation rate even for a homogeneous electron gas interacting with impurities or phonons. It is shown here that additional dependence of the spectral weight on a superconducting gap is very small in this model and this effect disappears totally when the relaxation rate is equal zero. The model metal with a single band is considered in details. It is well known that for this model there is the dependence of the sum rule on the temperature and the energy gap even in the case when the relaxation is absent. This dependence exists due to the smearing of the electron distribution function and it is expressed in the terms of Sommerfeld expansion. Here it is shown that these effects are considerably smaller than that of related with the relaxation rate if the band width is larger than the average phonon frequency. It is shown also that the experimental data about the temperature dependence of the spectral weight for the high- materials can be successfully explained in the framework approach based on the temperature dependence of the relaxation rateComment: 13 pages, 7 figures, the talk given on Internatinal coference on theoretical physics, april 11-16,2005, Mosco

Observation of the Holstein shift in high TcT_c superconductors with thermal modulation reflectometry

We use the experimental technique of thermal modulation reflectometry to study the relatively small temperature dependence of the optical conductivity of superconductors. Due to a large cancellation of systematic errors, this technique is shown to a be very sensitive probe of small changes in reflectivity. We analyze thermal modulation reflection spectra of single crystals and epitaxially grown thin films of YBa$_2$Cu$_3$O$_{7-\delta}$ and obtain the ${\alpha_tr}^2F(\omega)$ function in the normal state, as well as the superconductivity induced changes in reflectivity. We present detailed model calculations, based on the Eliashberg-Migdal extension of the BCS model, which show good qualitative and quantitative agreement with the experimental spectra. VSGD.93.12.thComment: 6 pages, figures on request. Revtex, version 2, Materials Science Center Internal Report Number VSGD.93.12.t

Far-infrared electrodynamics of superconducting Nb: comparison of theory and experiment

Complex conductivity spectra of superconducting Nb are calculated from the first principles in the frequency region around the energy gap and compared to the experimental results. The row experimental data obtained on thin films can be precisely described by these calculations.Comment: 4 pages, 3 eps figures incl. Accepted to Solid State Commu

Electromagnetic response of superconductors and optical sum rule

The interrelation between the condensation energy and the optical sum rules has been investigated. It has been shown that the so called 'partial' sum rule violation is related mainly to a temperature dependence of the relaxation rate rather than to the appearance of superconductivity itself. Moreover, we demonstrate that the experimental data on the temperature dependence of the optical sum rule can be explained rather well by an account of strong electron-phonon interaction.Comment: 16 pages, 1 figure. Submitted to Solid State Communication

Optical Sum Rule anomalies in the High-Tc Cuprates

We provide a brief summary of the observed sum rule anomalies in the high-T$_c$ cuprate materials. A recent issue has been the impact of a non-infinite frequency cutoff in the experiment. In the normal state, the observed anomalously high temperature dependence can be explained as a `cutoff effect'. The anomalous rise in the optical spectral weight below the superconducting transition, however, remains as a solid experimental observation, even with the use of a cutoff frequency.Comment: 4 pages, 2 figures, very brief review of optical sum rule anomal

Optical absorption in the strong coupling limit of Eliashberg theory

We calculate the optical conductivity of superconductors in the strong-coupling limit. In this anomalous limit the typical energy scale is set by the coupling energy, and other energy scales such as the energy of the bosons mediating the attraction are negligibly small. We find a universal frequency dependence of the optical absorption which is dominated by bound states and differs significantly from the weak coupling results. A comparison with absorption spectra of superconductors with enhanced electron-phonon coupling shows that typical features of the strong-coupling limit are already present at intermediate coupling.Comment: 10 pages, revtex, 4 uuencoded figure

Optical Sum Rule in Finite Bands

In a single finite electronic band the total optical spectral weight or optical sum carries information on the interactions involved between the charge carriers as well as on their band structure. It varies with temperature as well as with impurity scattering. The single band optical sum also bears some relationship to the charge carrier kinetic energy and, thus, can potentially provide useful information, particularly on its change as the charge carriers go from normal to superconducting state. Here we review the considerable advances that have recently been made in the context of high $T_c$ oxides, both theoretical and experimental.Comment: Review article accepted for publication in J. Low Temp. Phys. 29 pages, 33 figure