Detecting Superconductivity in the High Pressure Hydrides and Metallic Hydrogen from Optical Properties.

We present a new technique for measuring the critical temperature T_{c} in the high pressure, high T_{c} electron-phonon-driven superconducting hydrides. This technique does not require connecting leads to the sample. In the region of the absorption spectrum above the sum of the optical gap and maximum phonon energy, the reflectance mirrors the temperature variation of the superconducting order parameter. For an appropriately chosen value of fixed photon energy, the temperature dependence of the reflectance varies much more rapidly below T=T_{c} than above. It increases with increasing temperature in the superconducting state while it decreases in the normal state. Examining the temperature dependence of the reflectance at a fixed photon energy, there is a cusp at T=T_{c} which provides a measurement of the critical temperature. We discuss these issues within the context of the recently reported atomic metallic phase of hydrogen, but our proposed technique should prove useful for other hydrides with large coupling to high energy phonons.

Spectroscopic evidence of a new energy scale for superconductivity in H3S.

The discovery of a superconducting phase in sulfur hydride under high pressure with a critical temperature above 200 K has provided fresh impetus to the search for superconductors at ever higher temperatures. Although this systems displays all the hallmarks of superconductivity, the mechanism through which it arises remains to be determined. Here we provide a first optical spectroscopy study of this superconductor. Experimental results for the optical reflectivity of H3S, under hydrostatic pressure of 150 GPa, for several temperatures and over the range 60 to 600 meV of photon energies, are compared with theoretical calculations based on Eliashberg theory. Two significant features stand out: some remarkably strong infrared active phonons at around 160 meV, and a band with a depressed reflectance in the superconducting state in the region from 450 meV to 600 meV. In this energy range H3S becomes more reflecting with increasing temperature, a change that is traced to superconductivity originating from the electron-phonon interaction. The shape, magnitude, and energy dependence of this band at 150 K agrees with our calculations. This provides strong evidence of a conventional mechanism. However, the unusually strong optical phonon suggests a contribution of electronic degrees of freedom.

Electron-boson spectral density of LiFeAs obtained from optical data.

We analyze existing optical data in the superconducting state of LiFeAs at T = 4 K, to recover its electron-boson spectral density. A maximum entropy technique is employed to extract the spectral density I(2)χ(ω) from the optical scattering rate. Care is taken to properly account for elastic impurity scattering which can importantly affect the optics in an s-wave superconductor, but does not eliminate the boson structure. We find a robust peak in I(2)χ(ω) centered about Ω(R) ≅ 8.0 meV or 5.3 k(B)Tc (with Tc = 17.6 K). Its position in energy agrees well with a similar structure seen in scanning tunneling spectroscopy (STS). There is also a peak in the inelastic neutron scattering (INS) data at this same energy. This peak is found to persist in the normal state at T = 23 K. There is evidence that the superconducting gap is anisotropic as was also found in low temperature angular resolved photoemission (ARPES) data.

Optical spectroscopy of superconducting Ba0.55K0.45Fe2As2: evidence for strong coupling to low-energy bosons.

Normal state optical spectroscopy on single crystals of the new iron arsenide superconductor Ba0.55K0.45Fe2As2 shows that the infrared spectrum consists of two major components: a strong metallic Drude band and a well-separated midinfrared absorption centered at 0.7 eV. It is difficult to separate the two components unambiguously but several fits using Lorentzian peaks suggest a model with a Drude peak having a plasma frequency of 1.6 to 2.1 eV and a midinfrared peak with a plasma frequency of 2.5 eV. Detailed analysis of the frequency dependent scattering rate shows that the charge carriers interact with a broad bosonic spectrum extending beyond 100 meV with a very large coupling constant lambda=3.4 at low temperature. As the temperature increases this coupling weakens to lambda=0.78 at ambient temperature. This suggests a bosonic spectrum that is similar to what is seen in the lower Tc cuprates.

Exchange boson dynamics in cuprates: optical conductivity of HgBa_2CuO_4+delta.

The electron-boson spectral density function I;{2}chi(Omega) responsible for carrier scattering of the high temperature superconductor HgBa_{2}CuO_{4+delta} (T_{c}=90 K) is calculated from new data on the optical scattering rate. A maximum entropy technique is used. Published data on HgBa_{2}Ca_{2}Cu_{3}O_{8+delta} (T_{c}=130 K) are also inverted and these new results are put in the context of other known cases. All spectra (with two notable exceptions) show a peak at an energy (Omega_{r}) proportional to the superconducting transition temperature Omega_{r} approximately 6.3k_{B}T_{c}. This charge channel relationship follows closely the magnetic resonance seen by polarized neutron scattering, Omega_{r};{neutron} approximately 5.4k_{B}T_{c}. The amplitudes of both peaks decrease strongly with increasing temperature. In some cases, the peak at Omega_{r} is weak and the spectrum can have additional maxima and a background extending up to several hundred meV.

Bosonic spectral density of epitaxial thin-film La1.83Sr0.17CuO4 superconductors from infrared conductivity measurements.

We use optical spectroscopy to investigate the excitations responsible for the structure in the optical self-energy of thin epitaxial films of La(1.83)Sr(0.17)CuO(4). Using Eliashberg's formalism to invert the optical spectra we extract the electron-boson spectral function and find that at low temperature it has a two component structure closely matching the spin excitation spectrum recently measured by magnetic neutron scattering. We contrast the temperature evolution of the spectral density and the two-peak behavior in La(2-Sr(x)CuO(4) with another high temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+delta). The bosonic spectral functions of the two materials account for the low T(c) of LSCO as compared to Bi-2212.

Evidence for a pseudogap in underdoped Bi{2}Sr_{2}CaCu{2}O{8+delta} and YBa2Cu3O6.50 from in-plane optical conductivity measurements.

The real part of the in-plane optical self-energy data in underdoped Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} (Bi-2212) and ortho II YBa2Cu3O6.5 contains new and important information on the pseudogap. Using a theoretical model approach, a major new finding is that states lost below the pseudogap Delta_{pg} are accompanied by a pileup of states just above this energy. The pileup along with a sharp mode in the bosonic spectral function leads to an unusually rapid increase in the optical scattering rate as a function of frequency and a characteristically sloped peak in the real part of the optical self-energy. These features are not found in optimally doped and overdoped samples and represent the clearest signature so far in the in-plane optical conductivity of the opening of a pseudogap.

High energy scales in the optical self-energy of the cuprate superconductors.

Using optical spectroscopy with a derivative technique, we find for the high Tc cuprate Bi2Sr2CaCu2O8+delta (Bi-2212) evidence for a new high energy scale at 900 meV beyond the two previously well-known ones at roughly 50 and 400 meV. The intermediate scale at 400 meV has recently been seen in angle-resolved photoemission spectroscopy experiments along the nodal direction as a large kink. In YBa2Cu3O6.50, the three energy scales are shifted to lower energy relative to Bi-2212 and we observe the emergence of a possible new high energy feature at 600 meV.

A universal scaling relation in high-temperature superconductors.

Since the discovery of superconductivity at elevated temperatures in the copper oxide materials there has been a considerable effort to find universal trends and correlations amongst physical quantities, as a clue to the origin of the superconductivity. One of the earliest patterns that emerged was the linear scaling of the superfluid density (rho(s)) with the superconducting transition temperature (T(c)), which marks the onset of phase coherence. This is referred to as the Uemura relation, and it works reasonably well for the underdoped materials. It does not, however, describe optimally doped (where T(c) is a maximum) or overdoped materials. Similarly, an attempt to scale the superfluid density with the d.c. conductivity (sigma(dc)) was only partially successful. Here we report a simple scaling relation (rho(s) proportional, variant sigma(dc)T(c), with sigma(dc) measured at approximately T(c)) that holds for all tested high-T(c) materials. It holds regardless of doping level, nature of dopant (electrons versus holes), crystal structure and type of disorder, and direction (parallel or perpendicular to the copper-oxygen planes).

High-transition-temperature superconductivity in the absence of the magnetic-resonance mode.

The fundamental mechanism that gives rise to high-transition-temperature (high-T(c)) superconductivity in the copper oxide materials has been debated since the discovery of the phenomenon. Recent work has focused on a sharp 'kink' in the kinetic energy spectra of the electrons as a possible signature of the force that creates the superconducting state. The kink has been related to a magnetic resonance and also to phonons. Here we report that infrared spectra of Bi2Sr2CaCu2O8+delta (Bi-2212), shows that this sharp feature can be separated from a broad background and, interestingly, weakens with doping before disappearing completely at a critical doping level of 0.23 holes per copper atom. Superconductivity is still strong in terms of the transition temperature at this doping (T(c) approximately 55 K), so our results rule out both the magnetic resonance peak and phonons as the principal cause of high-T(c) superconductivity. The broad background, on the other hand, is a universal property of the copper-oxygen plane and provides a good candidate signature of the 'glue' that binds the electrons.

Oxygen isotope effect in the ab-plane reflectance of underdoped YBa(2)Cu(3)O(7-delta).

We have measured the effect of oxygen isotope substitution on the ab-plane reflectance of underdoped YBa(2)Cu(3)O(7-delta). The frequency shift of the transverse optic phonons due to the substitution of 16O by 18O yields an isotope effect of the expected magnitude for copper-oxygen stretching modes with alpha=0.5+/-0.1. The reflectance shoulder at 400-500 cm(-1) shows a much smaller exponent of alpha=0.1+/-0.1 in the normal state and alpha=0.23+/-0.1 in the superconducting state. These observations suggest that the shoulder is of electronic origin and not due to a phonon mode as has been suggested recently.

Transmittance of skew rays through metal light pipes.

The transmittance of skew rays through metal light pipes is examined with ray tracing. The transmittance with respect to pipe length is compared with analytical approximations and with experimental data. The effects of pipe material, pipe shape, wavelength of the incident light, distribution of the incident light, and maximum angle of incidence on transmittance are examined. The transmittance is shown, in general, not to be exponential with respect to pipe length. Additionally, the effect on transmittance of elbows and gaps in a pipe is investigated.