The smooth evolution of the tunneling gap of Bi2Sr2CaCu2O8 with doping from a pseudogap state in the underdoped cuprates to a superconducting state at optimal and overdoping, has been interpreted as evidence that the pseudogap must be due to precursor pairing. We suggest an alternative explanation, that the smoothness reflects a hidden SO(N) symmetry near the (π, 0) points of the Brillouin zone (with N = 3, 4, 5, or 6). Because of this symmetry, the pseudogap could actually be due to any of a number of nesting instabilities, including charge or spin density waves or more exotic phases.We present a detailed analysis of this competition for one particular model: the pinned Balseiro-Falicov model of competing charge density wave and (s-wave) superconductivity. We show that most of the anomalous features of both tunneling and photoemission follow naturally from the model, including the smooth crossover, the general shape of the pseudogap phase diagram, the shrinking Fermi surface of the pseudogap phase, and the asymmetry of the tunneling gap away from optimal doping. Below Tc, the sharp peak at ∆1 and the dip seen in the tunneling and photoemission near 2∆1 cannot be described in detail by this model, but we suggest a simple generalization to account for inhomogeneity, which does provide an adequate description.We show that it should be possible, with a combination of photoemission and tunneling, to demonstrate the extent of pinning of the Fermi level to the Van Hove singularity. A preliminary analysis of the data suggests pinning in the underdoped, but not in the overdoped regime.

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We analyze microwave cavity perturbation methods, and show that the technique is an excellent, precision method to study the dynamic magnetic and dielectric response in the GHz frequency range. Using superconducting cavities, we obtain exceptionally high precision and sensitivity for measurements of relative changes. A dynamic electromagnetic susceptibilitỹ ζ(T ) = ζ ′ + iζ ′′ is introduced, which is obtained from the measured parameters: the shift of cavity resonant frequency δf and quality factor Q. We focus on the case of a spherical sample placed at the center of a cylindrical cavity resonant in the T E011 mode. Depending on the sample characteristics, the magnetic permeabilityμ, the dielectric permittivityε and the complex conductivityσ can be extracted fromζH.A full spherical wave analysis of the cavity perturbation indicates that : (i) In highly insulating samples with dielectric constant ε ′ ∼ 1, the measuredζH ≈χM , enabling direct measurement of the magnetic susceptibility. The sensitivity of the method equals or surpasses that of dc SQUID measurements for the relative changes in magnetic susceptibility. (ii) For moderatẽ ε and conductivity σ,ζH ∝ε + iωσ/εo − 1, thus enabling direct measurement of the sample dielectric constantε, even though the sample is placed in a microwave magnetic field. (iii) For large σ we recover the surface impedance limit. (iv) Expressions are provided for the general case of a lossy dielectric represented byε + iωσ/εo. We show that an inversion procedure can be used to obtainε + iωσ/εo in a wide range of parameter values.This analysis has led to the observation of new phenomena in novel low dimensional materials. We discuss results on magneto-dynamics of the 3-D antiferromagnetic state of spin chain compound Sr2CuO3. In dielectric susceptibility measurements in Sr14Cu24O41, we directly observe a dielectric loss peak. Dimensional resonances in the paraelectric material SrT iO3 are shown to occur due to the rapid increase of dielectric constant with decreasing temperature. The cavity perturbation methods are thus an extremely sensitive probe of charge and spin dynamics in electronic materials. I IntroductionThe continuing discovery of new electronic materials calls for new methods of measuring their electric and magnetic properties. Microwave cavity perturbation techniques have proved to be very useful for the study of transport dynamics at microwave frequencies [1,2,3,4], in materials such as semiconductors, magnetic ferrites and exotic materials such as Charge and Spin Density Waves [5].In all of these previous studies normal metal cavities were used. To study the (then) newly discovered high temperature superconductors (HTS), the use of superconducting cavities was introduced by Sridhar and Kennedy [1]. The reduction in background absorption by a factor of 10 4 from a normal metal cavity enabled the measurement of absorption in small, single crystal superconductors and thin films. The surface impedanceZ s = R s − iX s was obtained in terms of changes of the cavity p...

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