A recent report that sulfur hydride under pressure is an electron-phonon superconductor with a Tc of 190 K has been met with much excitement although it is yet to be confirmed. Based on several electron-phonon spectral density functions already avail
able from density functional theory, we find that the electron-phonon spectrum is near optimum for Tc with a particularly large value of its characteristic phonon energy omega_ln which is due to the small hydrogen mass. We find that the thermodynamic universal BCS ratios are near those for Pb and Nb3Sn. We suggest that optical measurements could be a useful tool to establish the existence and nature of the superconductivity in this system. Conventional superconductors are in the impurity-dominated dirty limit. By contrast sulfur hydride will be in the clean limit because of its large energy gap scale. The AC optical conductivity will display distinct and separate signatures of the superconducting gap in the low-energy impurity-dominated range of the optical spectrum and additional phonon structures at higher energies where the clean limit applies.
We consider a model of the pseudogap specifically designed to describe the underdoped cuprates and which exhibits particle-hole asymmetry. The presence of electron pockets, besides the usual hole pockets, leads to the appearance of new vectors beyond
the usual so-called octet model in the joint density of states (JDOS), which underlies the analysis of Fourier-transform scanning tunneling spectroscopy (FT-STS) data. These new vectors are associated with distinct patterns of large amplitude in the JDOS and are expected to occur primarily at positive bias. Likewise a pseudogap Dirac point occurs at positive bias and this point can be determined either through FT-STS or through extrapolation of data from the autocorrelation function of angle-resolved photoemission spectroscopy.
The specific heat of the superconducting cuprates is calculated over the entire phase diagram. A d-wave BCS approach based on the large Fermi surface of Fermi liquid and band structure theory provides a good description of the overdoped region. At un
derdoping it is essential to include the emergence of a second energy scale, the pseudogap and its associated Gutzwiller factor, which accounts for a reduction in the coherent piece of the electronic Greens function due to increased correlations as the Mott insulating state is approached. In agreement with experiment, we find that the slope of the linear in T dependence of the low temperature specific heat rapidly increases above optimum doping while it is nearly constant below optimum. Our theoretical calculations also agree with recent data on Bi$_2$Sr$_{2-rm x}$La$_{rm x}$CuO$_{6+delta}$ for which the normal state is accessed through the application of a large magnetic field. A quantum critical point is located at a doping slightly below optimum.
The resonating valence bond spin liquid model for the underdoped cuprates has as an essential element, the emergence of a pseudogap. This new energy scale introduces asymmetry in the quasiparticle density of states because it is associated with the
antiferromagnetic Brillouin zone. By contrast, superconductivity develops on the Fermi surface and this largely restores the particle-hole symmetry for energies below the superconducting energy gap scale. In the highly underdoped regime, these two scales can be separately identified in the density of states and also partial density of states for each fixed angle in the Brillouin zone. From the total density of states, we find that the pseudogap energy scale manifests itself differently as a function of doping for positive and negative bias. Furthermore, we find evidence from recent scanning tunneling spectroscopy data for asymmetry in the positive and negative bias of the extracted $Delta(theta)$ which is in qualitative agreement with this model. Likewise, the slope of the linear low energy density of states is nearly constant in the underdoped regime while it increases significantly with overdoping in agreement with the data.
The penetration depth is calculated over the entire doping range of the cuprate phase diagram with emphasis on the underdoped regime. Pseudogap formation on approaching the Mott transition, for doping below a quantum critical point, is described with
in a model based on the resonating valence bond spin liquid which provides an ansatz for the coherent piece of the Greens function. Fermi surface reconstruction, which is an essential element of the model, has a strong effect on the superfluid density at T=0 producing a sharp drop in magnitude, but does not change the slope of the linear low temperature variation. Comparison with recent data on Bi-based cuprates provides validation of the theory and shows that the effects of correlations, captured by Gutzwiller factors, are essential for a qualitative understanding of the data. We find that the Ferrell-Glover-Tinkham sum rule still holds and we compare our results with those for the Fermi arc and the nodal liquid models.
New THz data on the optical conductivity of Pb are presented as well as a detailed Eliashberg analysis with particular emphasis on phonon-assisted processes not included in a BCS approach. Consideration of the optical self-energy instead of the condu
ctivity itself helps highlight the differences with BCS predictions. Predicted coherence peaks are observed in the optical scattering rates. Impurities enhance the optical effective mass at zero frequency by an order of magnitude and induce a large peak at twice the gap in agreement with theory. This work illustrates the usefulness of the optical self-energy for the analysis of data.
