CeCoIn5 - a quantum critical superfluid

We have made the first complete measurements of the London penetration depth $\lambda(T)$ of CeCoIn5, a quantum-critical metal where superconductivity arises from a non-Fermi-liquid normal state. Using a novel tunnel diode oscillator designed to avoid spurious contributions to $\lambda(T)$, we have established the existence of intrinsic and anomalous power-law behaviour at low temperature. A systematic analysis raises the possibility that the unusual observations are due to an extension of quantum criticality into the superconducting state.Comment: 5 pages, 3 figure

Apparatus for high resolution microwave spectroscopy in strong magnetic fields

We have developed a low temperature, high-resolution microwave surface impedance probe that is able to operate in high static magnetic fields. Surface impedance is measured by cavity perturbation of dielectric resonators, with sufficient sensitivity to resolve the microwave absorption of sub-mm-sized superconducting samples. The resonators are constructed from high permittivity single-crystal rutile (TiO2) and have quality factors in excess of 10^6. Resonators with such high performance have traditionally required the use of superconducting materials, making them incompatible with large magnetic fields and subject to problems associated with aging and power-dependent response. Rutile resonators avoid these problems while retaining comparable sensitivity to surface impedance. Our cylindrical rutile resonators have a hollow bore and are excited in TE_01(n-d) modes, providing homogeneous microwave fields at the center of the resonator where the sample is positioned. Using a sapphire hot-finger technique, measurements can be made at sample temperatures in the range 1.1 K to 200 K, while the probe itself remains immersed in a liquid helium bath at 4.2 K. The novel apparatus described in this article is an extremely robust and versatile system for microwave spectroscopy, integrating several important features into a single system. These include: operation at high magnetic fields; multiple measurement frequencies between 2.64 GHz and 14.0 GHz in a single resonator; excellent frequency stability, with typical drifts < 1 Hz per hour; the ability to withdraw the sample from the resonator for background calibration; and a small pot of liquid helium separate from the external bath that provides a sample base temperature of 1.1 K.Comment: 10 pages, 5 figure

Effect of realistic out-of-plane dopant potentials on the superfluid density of overdoped cuprates

Recent experimental papers on hole-doped overdoped cuprates have argued that a series of observations showing unexpected behavior in the superconducting state imply the breakdown of the quasiparticle-based Landau-BCS paradigm in that doping range. In contrast, some of the present authors have argued that a phenomenological "dirty $d$-wave" theoretical analysis explains essentially all aspects of thermodynamic and transport properties in the superconducting state, provided the unusual effects of weak, out-of-plane dopant impurities are properly accounted for. Here we attempt to place this theory on a more quantitative basis by performing $\textit{ab-initio}$ calculations of dopant impurity potentials for LSCO and Tl-2201. These potentials are more complex than the pointlike impurity models considered previously, and require calculation of forward scattering corrections to transport properties. Including realistic, ARPES-derived bandstructures, Fermi liquid renormalizations, and vertex corrections, we show that the theory can explain semiquantitatively the unusual superfluid density measurements of the two most studied overdoped materials.Comment: 19 page, 13 figure

Electrical transport measurements in the superconducting state of Bi2212 and Tl2201

Precise measurements of the in-plane microwave surface impedance of high-quality single crystals of Bi2212 and Tl2201 are used to probe the relaxation time of nodal quasiparticles in the d-wave superconducting state through a two-fluid analysis of the microwave conductivity. While this analysis requires us to posit a form for the frequency-dependent quasiparticle conductivity, we clearly demonstrate that the extraction of the relaxation rate is quite insensitive to the assumed shape of the quasiparticle spectrum. The robustness of the analysis is rooted in the oscillator-strength sum rule and the fact that we simultaneously measure the real and imaginary parts of the conductivity. In both Bi2212 and Tl2201 we infer a linear temperature dependence of the transport relaxation rate 1/tau and a small but finite zero-temperature intercept. The linear temperature dependence of 1/tau is in accord with expectations for weak elastic scattering in an unconventional superconductor with line nodes and a small residual density of states. The same analysis reveals an onset of inelastic scattering at higher temperatures similar to that seen in the YBCO superconductors. Finally we extrapolate the two-fluid model over a range of frequencies up to five times the measurement frequency, where the extrapolation predicts behaviour that is qualitatively similar to terahertz conductivity data on Bi2212 thin films. While relaxation rates in Bi2212 and Tl2201 are substantially higher than in YBCO there are qualitative similarities between all three materials, and the differences can likely be attributed to varying levels of static disorder. We therefore conclude that a universal picture of quasiparticle scattering in the cuprates is emerging.Comment: 10 pages, 9 figure

Phenomenology of a-axis and b-axis charge dynamics from microwave spectroscopy of highly ordered YBa2Cu3O6.50 and YBa2Cu3O6.993

Extensive measurements of the microwave conductivity of highly pure and oxygen-ordered \YBCO single crystals have been performed as a means of exploring the intrinsic charge dynamics of a d-wave superconductor. Broadband and fixed-frequency microwave apparatus together provide a very clear picture of the electrodynamics of the superconducting condensate and its thermally excited nodal quasiparticles. The measurements reveal the existence of very long-lived excitations deep in the superconducting state, as evidenced by sharp cusp-like conductivity spectra with widths that fall well within our experimental bandwidth. We present a phenomenological model of the microwave conductivity that captures the physics of energy-dependent quasiparticle dynamics in a d-wave superconductor which, in turn, allows us to examine the scattering rate and oscillator strength of the thermally excited quasiparticles as functions of temperature. Our results are in close agreement with the Ferrell-Glover-Tinkham sum rule, giving confidence in both our experiments and the phenomenological model. Separate experiments for currents along the $\hat a$ and $\hat b$ directions of detwinned crystals allow us to isolate the role of the CuO chain layers in \YBCO, and a model is presented that incorporates both one-dimensional conduction from the chain electrons and two-dimensional transport associated with the \cuplane plane layers.Comment: 17 pages, 13 figure

Observation of the Transverse Optical Plasmon in SmLa0.8Sr0.2CuO4-d

We present microwave and infrared measurements on SmLa0.8Sr0.2CuO4-d, which are direct evidence for the existence of a transverse optical plasma mode, observed as a peak in the c-axis optical conductivity. This mode appears as a consequence of the existence of two different intrinsic Josephson couplings between the CuO2 layers, one with a Sm2O2 block layer, and the other one with a (La,Sr)O block layer. From the frequencies and the intensities of the collective modes we determine the value of the compressibility of the two dimensional electron fluid in the copper oxygen planes.Comment: REVTeX, 4 pages, 5 eps-figures, PRL, in pres

Non-Locality and Strong Coupling in the Heavy Fermion Superconductor CeCoIn5_{5}: A Penetration Depth Study

We report measurements of the magnetic penetration depth $\lambda$ in single crystals of CeCoIn$_{5}$ down to $\sim$0.14 K using a tunnel-diode based, self-inductive technique at 28 MHz. While the in-plane penetration depth tends to follow a power law, $\lambda_{//} \sim {\it T}^{3/2}$, the data are better described as a crossover between linear ({\it T} $\gg$ ${\it T}^\ast$) and quadratic ({\it T} $\ll {\it T}^\ast$) behavior, with ${\it T}^\ast$ the crossover temperature in the strong-coupling limit. The {\it c}-axis penetration depth $\lambda_{\perp}$ is linear in {\it T}, providing evidence that CeCoIn$_{5}$ is a {\it d}-wave superconductor with line nodes along the {\it c}-axis. The different temperature dependences of $\lambda_{//}$ and $\lambda_{\perp}$ rule out impurity effects as the source of ${\it T}^{\ast}$.Comment: 4 pages, 3 figure

Microwave Spectroscopy of Thermally Excited Quasiparticles in YBa_2Cu_3O_{6.99}

We present here the microwave surface impedance of a high purity crystal of $YBa_2Cu_3O_{6.99}$ measured at 5 frequencies between 1 and 75 GHz. This data set reveals the main features of the conductivity spectrum of the thermally excited quasiparticles in the superconducting state. Below 20 K there is a regime of extremely long quasiparticle lifetimes, due to both the collapse of inelastic scattering below $T_c$ and the very weak impurity scattering in the high purity $BaZrO_3$-grown crystal used in this study. Above 20 K, the scattering increases dramatically, initially at least as fast as $T^4$.Comment: 13 pages with 10 figures. submitted to Phys Rev