Cuprate high- T _c superconductors exhibit enigmatic behavior in the nonsuperconducting state. For carrier concentrations near “optimal doping” (with respect to the highest T _c s) the transport and spectroscopic properties are unlike those of a Landau–Fermi liquid. On the Mott-insulating side of the optimal carrier concentration, which corresponds to underdoping, a pseudogap removes quasi-particle spectral weight from parts of the Fermi surface and causes a breakup of the Fermi surface into disconnected nodal and antinodal sectors. Here, we show that the near-nodal excitations of underdoped cuprates obey Fermi liquid behavior. The lifetime τ ( ω , T ) of a quasi-particle depends on its energy ω as well as on the temperature T . For a Fermi liquid, 1/ τ ( ω , T ) is expected to collapse on a universal function proportional to ( ℏω ) ² + ( pπk _B T ) ² . Magneto-transport experiments, which probe the properties in the limit ω = 0, have provided indications for the presence of a T ² dependence of the dc ( ω = 0) resistivity of different cuprate materials. However, Fermi liquid behavior is very much about the energy dependence of the lifetime, and this can only be addressed by spectroscopic techniques. Our optical experiments confirm the aforementioned universal ω - and T dependence of 1/ τ ( ω , T ), with p ∼ 1.5. Our data thus provide a piece of evidence in favor of a Fermi liquid-like scenario of the pseudogap phase of the cuprates.

Background: Color traits in animals play crucial roles in thermoregulation, photoprotection, camouflage, and visual communication, and are amenable to objective quantification and modeling. However, the extensive variation in non-melanic pigments and structural colors in squamate reptiles has been largely disregarded. Here, we used an integrated approach to investigate the morphological basis and physical mechanisms generating variation in color traits in tropical day geckos of the genus Phelsuma. Results: Combining histology, optics, mass spectrometry, and UV and Raman spectroscopy, we found that the extensive variation in color patterns within and among Phelsuma species is generated by complex interactions between, on the one hand, chromatophores containing yellow/red pteridine pigments and, on the other hand, iridophores producing structural color by constructive interference of light with guanine nanocrystals. More specifically, we show that 1) the hue of the vivid dorsolateral skin is modulated both by variation in geometry of structural, highly ordered narrowband reflectors, and by the presence of yellow pigments, and 2) that the reflectivity of the white belly and of dorsolateral pigmentary red marks, is increased by underlying structural disorganized broadband reflectors. Most importantly, these interactions require precise colocalization of yellow and red chromatophores with different types of iridophores, characterized by ordered and disordered nanocrystals, respectively. We validated these results through numerical simulations combining pigmentary components with a multilayer interferential optical model. Finally, we show that melanophores form dark lateral patterns but do not significantly contribute to variation in blue/green or red coloration, and that changes in the pH or redox state of pigments provide yet another source of color variation in squamates. Conclusions: Precisely colocalized interacting pigmentary and structural elements generate extensive variation in lizard color patterns. Our results indicate the need to identify the developmental mechanisms responsible for the control of the size, shape, and orientation of nanocrystals, and the superposition of specific chromatophore types. This study opens up new perspectives on Phelsuma lizards as models in evolutionary developmental biology.

We report the influence on the superconducting critical temperature T_c in doped SrTiO₃ of the substitution of the natural ¹⁶O atoms by the heavier isotope ¹⁸O. We observe that for a wide range of doping this substitution causes a strong (~50%) enhancement of T_c. Also the magnetic critical field H_c2 is increased by a factor ~2. Such a strong impact on T_c and H_c2, with a sign opposite to conventional superconductors, is unprecedented. The observed effect could be the consequence of strong coupling of the doped electrons to lattice vibrations (phonons), a notion which finds support in numerous optical and photo-emission studies. The unusually large size of the observed isotope effect supports a recent model for superconductivity in these materials based on strong coupling to the ferroelectric soft modes of SrTiO₃.

The soft ferroelectric phonon in ${\mathrm{SrTiO}}_3$ observed with optical spectroscopy has an extraordinarily strong spectral weight which is much stronger than expected in the limit of a perfectly ionic compound. This “charged phonon” effect in ${\mathrm{SrTiO}}_3$ is caused by the close-to-covalent character of the Ti-O ionic bond and implies a strong coupling between the soft ferroelectric phonon and the interband transitions across the 3-eV gap of ${\mathrm{SrTiO}}_3$. We demonstrate that this coupling leads, in addition to the charged phonon effect, to a pairing interaction involving the exchange of two transverse optical phonons. This process owes its relevance to the strong electron-phonon coupling and to the fact that the interaction mediated by a single transverse optical phonon vanishes at low electron density. We use the experimental soft phonon spectral weight to calculate the strength of the biphonon mediated pairing interaction in the electron-doped material and show that it is of the correct magnitude when compared to the experimental value of the superconducting critical temperature. Biphonon exchange is therefore an important pairing mechanism at low doping, and may be the key to understanding the occurrence of superconductivity in doped ${\mathrm{SrTiO}}_3$ and other low electron density materials.

Materials tuned to a quantum critical point display universal scaling properties as a function of temperature T and frequency ω. A long-standing puzzle regarding cuprate superconductors has been the observed power-law dependence of optical conductivity with an exponent smaller than one, in contrast to T-linear dependence of the resistivity and ω-linear dependence of the optical scattering rate. Here, we present and analyze resistivity and optical conductivity of La_2−xSr_xCuO₄ with x = 0.24. We demonstrate ℏω/k_BT scaling of the optical data over a wide range of frequency and temperature, T-linear resistivity, and optical effective mass proportional to $$\sim \ln T$$~ ln T corroborating previous specific heat experiments. We show that a T, ω-linear scaling Ansatz for the inelastic scattering rate leads to a unified theoretical description of the experimental data, including the power-law of the optical conductivity. This theoretical framework provides new opportunities for describing the unique properties of quantum critical matter.

We performed an experimental study of the temperature and doping dependence of the energy-loss function of the bilayer and trilayer bismuth cuprates family. The primary aim is to obtain information on the energy stored in the Coulomb interaction between the conduction electrons, on the temperature dependence thereof, and on the change of Coulomb interaction when Cooper pairs are formed. We performed temperature-dependent ellipsometry measurements on several ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8-x}$ single crystals: underdoped with $T_c=60$, 70, and 83 K; optimally doped with $T_c=91\mathrm{K}$; overdoped with $T_c=84$, 81, 70, and 58 K; as well as optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{10+x}$ with $T_c=110\mathrm{K}$. Our first observation is that, as the temperature drops through $T_c$, the loss function in the range up to 2 eV displays a change of temperature dependence as compared to the temperature dependence in the normal state. This effect at—or close to—$T_c$ depends strongly on doping, with a sign change for weak overdoping. The size of the observed change in Coulomb energy, using an extrapolation with reasonable assumptions about its $q$ dependence, is about the same size as the condensation energy that has been measured in these compounds. Our results therefore lend support to the notion that the Coulomb energy is an important factor for stabilizing the superconducting phase. Because of the restriction to small momentum, our observations do not exclude a possible significant contribution to the condensation energy of the Coulomb energy associated with the region of $q$ around $(\pi ,\pi )$.