a-b Plane Microwave Surface Impedance of a High-Quality Bi2Sr2CaCu2O8 Single Crystal

Mapping Dynamical Magnetic Responses of Ultrathin Micron-Size Superconducting Films Using Nitrogen-Vacancy Centers in Diamond

Two-dimensional superconductors have attracted growing interest because of their scientific novelty, structural tunability, and useful properties. Studies of their magnetic responses, however, are often hampered by difficulties to grow large-size samples of high quality and uniformity. We report here an imaging method that employed NV^- centers in diamond as a sensor capable of mapping out the microwave magnetic field distribution on an ultrathin superconducting film of micron size. Measurements on a 33 nm thick film and a 125 nm thick bulklike film of Bi₂Sr₂CaCu₂O_8+δ revealed that the alternating current (ac) Meissner effect (or repulsion of ac magnetic field) set in at 78 and 91 K, respectively; the latter was the superconducting transition temperature of both films. The unusual ac magnetic response of the thin film presumably was due to thermally excited vortex-antivortex diffusive motion in the film. Spatial resolution of our ac magnetometer was limited by optical diffraction and the noise level was at 14 μT/Hz^1/2. The technique could be extended with better detection sensitivity to extract local ac conductivity/susceptibility of ultrathin or monolayer superconducting samples as well as ac magnetic responses of other two-dimensional exotic thin films of limited lateral size.

Doping dependent evolution of magnetism and superconductivity in Eu(1-x)K(x)Fe2As2 (x = 0-1) and temperature dependence of the lower critical field H(c1)

We have synthesized polycrystalline samples of Eu(1-x)K(x)Fe2As2 (x = 0-1) and carried out systematic characterization using x-ray diffraction, ac and dc magnetic susceptibility, and electrical resistivity measurements. A clear signature of the coexistence of a superconducting transition (T(c) = 5.5 K) with spin density wave (SDW) ordering is observed in our underdoped sample with x = 0.15. The SDW transition disappears completely for the x = 0.3 sample and superconductivity arises below 20 K. The superconducting transition temperature Tc increases with increase in the K content and a maximum Tc = 33 K is reached for x = 0.5, beyond which it decreases again. The doping dependent Tx phase diagram is extracted from the magnetic and electrical transport data. It is found that magnetic ordering of Eu moments coexists with the superconductivity up to x = 0.6. The isothermal magnetization data taken at 2 K for the doped samples suggest the 2+ valence state of the Eu ions. We also present the temperature dependence of the lower critical field H(c1) of the superconducting polycrystalline samples. The values of H(c1)(0) obtained for x = 0.3, 0.5, and 0.7 after taking the demagnetization factor into account are 202, 330, and 212 Oe, respectively. The London penetration depth λ(T) calculated from the lower critical field does not show exponential dependence at low temperature, as would be expected for a fully gapped clean s-wave superconductor. In contrast, it shows a T2 power law feature up to T = 0.3Tc, as observed in Ba(1-x)K(x)Fe2As2 and BaFe(2-x)Co(x)As2.

Phase fluctuations in a strongly disordered s-wave NbN superconductor close to the metal-insulator transition

We explore the role of phase fluctuations in a three-dimensional s-wave superconductor, NbN, as we approach the critical disorder for destruction of the superconducting state. Close to critical disorder, we observe a finite gap in the electronic spectrum which persists at temperatures well above T(c). The superfluid density is strongly suppressed at low temperatures and evolves towards a linear-T variation at higher temperatures. These observations provide strong evidence that phase fluctuations play a central role in the formation of a pseudogap state in a disordered s-wave superconductor.

Specific heat evidence for bulk s-wave gap symmetry of optimally electron-doped Pr(1.85)Ce(0.15)CuO(4-y) superconductors

We reanalyze specific heat data for optimally electron-doped Pr(1.85)Ce(0.15)CuO(4-y) superconductors. The magnetic field dependence of the electronic specific heat in the vortex state does not support d-wave gap symmetry but agrees quantitatively with an s-wave theory. Furthermore, the field dependence at a finite temperature almost coincides with that for a conventional s-wave superconductor, Vi(3)Si. The present work provides bulk evidence for a nodeless s-wave gap symmetry in optimally electron-doped cuprates.

London penetration depth in the tight binding approximation: orthorhombic distortion and oxygen isotope effects in cuprates

We present a simple derivation of an expression for the superfluid density n(s) α 1/λ(2) in superconductors with the tight binding energy dispersion. The derived expression is discussed in detail because of its distinction from the known expressions for ordinary superconductors with parabolic energy dispersion. We apply this expression for the experimental data analysis of the isotope effect in London penetration depth parameter λ in the BiSrCuO and YBaCuO family compounds near optimal doping, taking into account the orthorhombic distortion of crystal structure, and estimate the isotopic change of hopping parameters from the experimental data. We point out that 1/λ(2) temperature behaviour is very sensitive to the ratio 2Δ(m)(T = 0)/k(B)T(c) and estimate this quantity for a number of compounds.

Kosterlitz-Thouless behavior in layered superconductors: the role of the vortex core energy

In layered superconductors (SC) with small interlayer Josephson coupling vortex-antivortex phase fluctuations characteristic of quasi two-dimensional (2D) Kosterlitz-Thouless behavior are expected to be observable at some energy scale T(d). While in the 2D case T(d) is uniquely identified by the KT temperature T(KT) where the universal value of the superfluid density is reached, we show that in a generic anisotropic 3D system T(d) is controlled by the vortex-core energy, and can be significantly larger than the 2D scale T(KT). These results are discussed in relation to recent experiments in cuprates, which represent a typical experimental realization of layered anisotropic SC.

Evidence for a nodeless gap from the superfluid density of optimally doped Pr(1.855)Ce(0.145)CuO(4-y) films

We present measurements of the ab-plane magnetic penetration depth, lambda(T), in five optimally doped Pr(1.855)Ce(0.145)CuO(4-y) films for 1.6 K< or =T < or =T(c) approximately 24 K. Low resistivities, high superfluid densities n(s)(T) proportional, variant lambda(-2)(T), high T(c)'s, and small transition widths are reproducible and indicative of excellent film quality. For all five films, lambda(-2)(T)/lambda(-2)(0) at low T is well fitted by an exponential temperature dependence with a gap, Delta(min), of 0.85k(B)T(c). This behavior is consistent with a nodeless gap and is incompatible with d-wave superconductivity.

Projected wave functions and high temperature superconductivity

We study the Hubbard model with parameters relevant to cuprates using variational Monte Carlo for projected d-wave states. For doping 0<x approximately less than or equal to 0.35 we obtain a superconductor whose order parameter Phi(x) tracks the observed nonmonotonic T(c)(x). The variational parameter Delta(var)(x) scales with the (pi,0) "hump" and T* seen in photoemission. Projection leads to incoherence in the spectral function and from the singular behavior of its moments we obtain the nodal quasiparticle weight Z approximately x though the Fermi velocity remains finite as x-->0. The Drude weight D(low) and superfluid density are consistent with experiment and D(low) approximately Z.

Effects of vortex pinning and thermal fluctuations on the Josephson plasma resonance in Tl2Ba2CaCu2O8 and YBa2Cu3O6.5

We investigated the temperature dependence and c-axis magnetic field dependence of the Josephson plasma resonance in optimally doped Tl2Ba2CaCu2O8 thin films and underdoped YBa2Cu3O6.5 (YBCO) ortho-II single crystals using infrared spectroscopy. We obtained the c-axis penetration depths, at low temperature, in zero fields of about 20 and 7 microm, respectively. While the temperature dependencies of the resonances in the two compounds are very similar, the magnetic field dependence in YBCO is much weaker. We attribute this weak magnetic field dependence to the lower anisotropy of YBCO and interpret the observed behaviors in terms of thermal fluctuations and pinning of pancake vortices.

Evidence for nodal quasiparticles in electron-doped cuprates from penetration depth measurements

The in-plane magnetic penetration depth, lambda(T), was measured down to 0.4 K in single crystals of electron-doped superconductors, Pr(1.85)Ce(0.15)CuO(4-delta) (PCCO) and Nd(1.85)Ce(0.15)CuO(4-delta) (NCCO). In PCCO, the superfluid density varies as T2 from 0.025 up to roughly 0.3T/T(c) suggestive of a d-wave state with impurities. In NCCO, lambda(T) shows a pronounced upturn for T<4 K due to the paramagnetic contribution of Nd3+ ions. Fits to an s-wave order parameter over the standard BCS range (T/T(c) = 0.32) limit any gap to less than Delta(min)(0)/T(c) = 0.57 in NCCO. For PCCO, the absence of paramagnetism permits a lower temperature fit and yields an upper limit of Delta(min)(0)/T(c) = 0.2.

Microwave electrodynamics of electron-doped cuprate superconductors

We report microwave cavity perturbation measurements of the temperature dependence of the penetration depth, lambda(T), and conductivity, sigma(T) of Pr(2-x)Ce(x)CuO(4-delta) (PCCO) crystals, as well as parallel-plate resonator measurements of lambda(T) in PCCO thin films. Penetration depth measurements are also presented for a Nd(2-x)Ce(x)CuO(4-delta) (NCCO) crystal. We find that Deltalambda(T) has a power-law behavior for T<T(c)/3, and conclude that the electron-doped cuprate superconductors have nodes in the superconducting gap. Furthermore, using the surface impedance, we have derived the real part of the conductivity, sigma(1)(T), below T(c) and found a behavior similar to that observed in hole-doped cuprates.

Nodal quasiparticle lifetime in the superconducting state of Bi(2)Sr(2)CaCu(2)O(8+delta)

We have measured the complex conductivity sigma of a Bi(2)Sr(2)CaCu(2)O(8+delta) thin film between 0.2 and 0.8 THz. We find sigma in the superconducting state to be well described as the sum of contributions from quasiparticles, condensate, and order parameter fluctuations which draw 30% of the spectral weight from the condensate. An analysis based on this decomposition yields a quasiparticle scattering rate on the order of k(B)T/Planck's over 2pi for temperatures below T(c).

Role of Nd/Ba disorder on the penetration depth of Nd(1+x)Ba(2-x)Cu(3)O(7-delta) thin films

We report on a study on the effect of Nd/Ba disorder on the ab-plane penetration depth of epitaxial Nd(1+x)Ba(2-x)Cu(3)O(7-delta) thin films. While in stoichiometric samples lambda(T) at low temperature is linear, Nd-rich films exhibit a quadratic law. For low Nd excess (x<0.04), a satisfying fit is obtained using the "dirty" d-wave model assuming that Nd ions at Ba sites act as strong scattering centers. At high x (x>0.15) the data are explained if Nd/Ba disorder becomes less effective as a source of scattering. The effect of localization has been discussed to account for the experimental results.

Evidence for coexistence of the superconducting gap and the pseudogap in Bi-2212 from intrinsic tunneling spectroscopy

We present intrinsic tunneling spectroscopy measurements on small Bi2Sr2CaCu2O8+x mesas. The tunnel conductance curves show both sharp peaks at the superconducting gap voltage and broad humps representing the c-axis pseudogap. The superconducting gap vanishes at Tc, while the pseudogap exists both above and below Tc. Our observation implies that the superconducting and pseudogaps represent different coexisting phenomena.

Advances in the physics of high-temperature superconductivity

The high-temperature copper oxide superconductors are of fundamental and enduring interest. They not only manifest superconducting transition temperatures inconceivable 15 years ago, but also exhibit many other properties apparently incompatible with conventional metal physics. The materials expand our notions of what is possible, and compel us to develop new experimental techniques and theoretical concepts. This article provides a perspective on recent developments and their implications for our understanding of interacting electrons in metals.

Atomic-scale quasi-particle scattering resonances in Bi2Sr2CaCu2O8+delta

Low-temperature scanning tunneling spectroscopy of the high transition temperature (high-Tc) cuprate Bi2Sr2CaCu2O8+delta reveals the existence of large numbers of identical regions with diameters of about 3 nanometers that have a relatively high density of low-energy quasi-particle states. Their spatial and spectroscopic characteristics are consistent with theories of strong quasi-particle scattering from atomic-scale impurities in a d-wave superconductor. These characteristics include breaking of local particle-hole symmetry, a diameter near twice the superconducting coherence length, and an inverse square dependence of their local density-of-states on distance from the scattering center. In addition to the validation of d-wave quasi-particle scattering theories, these observations identify a source for the anomalously high levels of low-energy quasi-particles in Bi2Sr2CaCu2O8+delta at low temperatures.