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International audience; Type II superconductors with high upper critical fields H c2 have considerable potential for practical applications, including high magnetic field solenoids, permanent magnets and energy storage devices, as well as magnetic field detectors (SQUID's) and superconducting components for electronics and communications. However, the interplay between electrical currents and lines of quantised magnetic flux (the "flux lines", "vortex lines", or simply "vortices" of Section A.2.3.3), in superconducting materials results in a driving force that puts the latter in motion. Vortex motion leads to dissipation of energy, manifested as an electric potential within the material, which therefore can no longer be considered to be superconducting, i.e. its electrical resistance becomes non-zero [Bardeen and Stephen 1965]. Preventing vortex motion up to a high critical current density j c is therefore essential. This is achieved through pinning of the vortex lines by imperfections of the material. Fortunately, such flux pinning is a general phenomenon in commonly produced materials. In the following sections an overview is given of this interesting phenomenon and some related issues. A3.2.2 Origin of flux pinning : material defects and flux pinning interactions

In a sandwich consisting of two superconducting films, one weakly pinning and one strongly pinning, the vortex positions in both films are determined by the strongly pinning material and the vortex lattice is disordered in both films. We used (strongly pinning) NbN and (weakly pinning) MoGe and studied, by directly imaging the vortex core positions with a scanning tunnelling microscope, how this disorder is restored with increasing thickness of MoGe layer or when the interface is made insulating. For clean interfaces we find that the first reordering of the vortex lattice is found at a layer thickness wich is compatible with the first bending mode of the vortex lines. Making the interface insulating we find that order is restored quickly. We argue that this is can be understood from the competition between the Josephson force working on the vortex segments on the one hand, and the elastic restoring forces inside the weakly pinning layer on the other hand., 7 pages, 9 figures

We present the ab-plane optical conductivity of four single crystals of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212) with different carrier doping levels from the strongly underdoped to the strongly overdoped range with $T_c$=66, 88, 77, and 67 K respectively. We focus on the redistribution of the low frequency optical spectral weight (SW) in the superconducting and normal states. The temperature dependence of the low-frequency spectral weight in the normal state is significantly stronger in the overdoped regime. In agreement with other studies, the superconducting order is marked by an increase of the low frequency SW for low doping, while the SW decreases for the highly overdoped sample. The effect crosses through zero at a doping concentration $\delta$=0.19 which is slightly to the right of the maximum of the superconducting dome. This sign change is not reproduced by the BCS model calculations, assuming the electron-momentum dispersion known from published ARPES data. Recent Cluster Dynamical Mean Field Theory (CDMFT) calculations based on the Hubbard and t-J models, agree in several relevant respects with the experimental data.

The Josephson Plasma Resonance is used to study the c-axis supercurrent in the superconducting state of underdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+��}$ with varying degrees of controlled point-like disorder, introduced by high-energy electron irradiation. As disorder is increased, the Josephson Plasma frequency decreases proportionally to the critical temperature. The temperature dependence of the plasma frequency does not depend on the irradiation dose, and is in quantitative agreement with a model for quantum fluctuations of the superconducting phase in the CuO$_{2}$ layers., 2 pages, submitted to the Proceedings of M2S-HTSC VIII Dresden

We present the ab-plane optical conductivity of four single crystals of Bi2Sr2CaCu2O8+δ(Bi2212) with different carrier doping levels from the strongly underdoped to the strongly overdoped range with Tc=66, 88, 77, and 67K, respectively. We focus on the redistribution of the low frequency optical spectral weight (SW) in the superconducting and normal states. The temperature dependence of the low-frequency spectral weight in the normal state is significantly stronger in the overdoped regime. In agreement with other studies, the superconducting order is marked by an increase of the low frequency SW for low doping, while the SW decreases for the highly overdoped sample. The effect crosses through zero at a doping concentration δ=0.19 which is slightly to the right of the maximum of the superconducting dome. This sign change is not reproduced by the BCS model calculations, assuming the electron-momentum dispersion known from ARPES data. Recent cluster dynamical mean field theory calculations based on the Hubbard and t−J models, agree in several relevant respects with the experimental data.

We present the ab-plane optical conductivity of four single crystals of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+��}$ (Bi2212) with different carrier doping levels from the strongly underdoped to the strongly overdoped range with $T_c$=66, 88, 77, and 67 K respectively. We focus on the redistribution of the low frequency optical spectral weight (SW) in the superconducting and normal states. The temperature dependence of the low-frequency spectral weight in the normal state is significantly stronger in the overdoped regime. In agreement with other studies, the superconducting order is marked by an increase of the low frequency SW for low doping, while the SW decreases for the highly overdoped sample. The effect crosses through zero at a doping concentration $��$=0.19 which is slightly to the right of the maximum of the superconducting dome. This sign change is not reproduced by the BCS model calculations, assuming the electron-momentum dispersion known from published ARPES data. Recent Cluster Dynamical Mean Field Theory (CDMFT) calculations based on the Hubbard and t-J models, agree in several relevant respects with the experimental data.

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., 10 pages, 9 figures

The introduction of a large density of columnar defects in %underdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ crystals does not, at sufficiently low vortex densities, increase the irreversibility line beyond the first order transition (FOT) field of pristine crystals. At such low fields, the flux line wandering length $r_{w}$ behaves as in pristine %Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ crystals. Next, vortex positional correlations along the $c$--axis in the vortex Bose glass at fields above the FOT are smaller than in the low--field vortex solid. Third, the Bose-glass-to-vortex liquid transition is signaled by a rapid decrease in c-axis phase correlations. These observations are understood in terms of the ``discrete superconductor'' model., Comment: 4 pages, 4 figures Submitted to Phys. Rev. B Rapid Comm. 16-1-2004 Revised version 18-3-2004

Using 30 MeV C60 fullerene irradiation, we have produced latent tracks of diameter 20 nm and length 200 nm, near the surface of single crystalline Bi2Sr2CaCu2O8+d. A preliminary transmission electron microscopy study shows evidence for a very high density of deposited energy, and the ejection of material from the track core in very thin specimens. The latent tracks reveal themselves to be exceptionally strong pinning centers for vortices in the superconducting mixed state. Both the critical current density and magnetic irreversibility line are significantly enhanced. The irradiated crystals present salient features of the (B,T) phase diagram of vortex matter both of pristine crystals, such as the first order vortex phase transition, and the exponential Bose-glass line characteristic of heavy ion-irradiated crystals. We show that the latter is manifestly independent of the pinning potential

The introduction of a large density of columnar defects in %underdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+��}$ crystals does not, at sufficiently low vortex densities, increase the irreversibility line beyond the first order transition (FOT) field of pristine crystals. At such low fields, the flux line wandering length $r_{w}$ behaves as in pristine %Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+��}$ crystals. Next, vortex positional correlations along the $c$--axis in the vortex Bose glass at fields above the FOT are smaller than in the low--field vortex solid. Third, the Bose-glass-to-vortex liquid transition is signaled by a rapid decrease in c-axis phase correlations. These observations are understood in terms of the ``discrete superconductor'' model., 4 pages, 4 figures Submitted to Phys. Rev. B Rapid Comm. 16-1-2004 Revised version 18-3-2004

In certain materials with strong electron correlations a quantum phase transition (QPT) at zero temperature can occur, in the proximity of which a quantum critical state of matter has been anticipated. This possibility has recently attracted much attention because the response of such a state of matter is expected to follow universal patterns defined by the quantum mechanical nature of the fluctuations. Forementioned universality manifests itself through power-law behaviours of the response functions. Candidates are found both in heavy fermion systems and in the cuprate high Tc superconductors. Although there are indications for quantum criticality in the cuprate superconductors, the reality and the physical nature of such a QPT are still under debate. Here we identify a universal behaviour of the phase angle of the frequency dependent conductivity that is characteristic of the quantum critical region. We demonstrate that the experimentally measured phase angle agrees precisely with the exponent of the optical conductivity. This points towards a QPT in the cuprates close to optimal doping, although of an unconventional kind., pdf format, 9 pages, 4 color figures included

Using differential magneto-optical imaging, we address the question of mesoscopic inhomogeneity in underdoped Bi-2212 single crystals. Among other features, it is shown that an anomalous temperature dependence of the penetration field and of the first order transition (FOT) field of the vortex lattice in such crystals can be understood as arising from inhomogeneity. The effect of chemical inhomogeneity and pinning on flux penetration and the FOT is discussed., Comment: Proceedings of the NATO Advanced Research Workshop on Magneto-Optical Imaging Oystese, Norway, August 27th - August 31st, 2003 (Kluwer) (8 pages) Corrected axis on Figure 3

Vortex thermal fluctuations in heavily underdoped Bi2Sr2CaCu2O8+d (Tc=69.4 K) are studied using Josephson plasma resonance (JPR). From the data in zero magnetic field, we obtain the penetration depth along the c-axis, lambda_{L,c}(0) = 229 micrometers and the anisotropy ratio gamma(0) = 600. The low plasma frequency allows us to study phase correlations over the whole vortex solid (Bragg-glass) state. The JPR results yield a wandering length r_{w} of vortex pancakes. The temperature dependence of r_{w} as well as its increase with applied dc magnetic field can only be explained by the renormalization of the tilt modulus by thermal fluctuations, and suggest the latter is responsible for the dissociation of the vortices at the first order transition., Comment: 4 pages, 5 figures. Submitted to Phys. Rev. Lett

Interlayer tunneling resistivity is used to probe the low-energy density-of-states (DOS) depletion due to the pseudogap in the normal state of Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$. Measurements up to 60 T reveal that a field that restores DOS to its ungapped state shows strikingly different temperature and doping dependencies from the characteristic fields of the superconducting state. The pseudogap closing field and the pseudogap temperature $T^{\star}$ evaluated independently are related through a simple Zeeman energy scaling. These findings indicate a predominant role of spins over the orbital effects in the formation of the pseudogap., Comment: 5 pages, 4 figures, presented at the APS March 2001 meeting, will appear in Phys. Rev. Lett

Dynamic and thermodynamic magnetization experiments on heavy-ion irradiated single crystalline Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta} are correlated in order to clarify the nature of the mixed state phase diagram. It is shown that whereas the entropy contribution to the free energy in the London regime plays a minor role in unirradiated crystals and irradiated crystals at fields close to or above the matching field $B_{\phi}$, it becomes very important at low fields in irradiated crystals with high $B_{\phi}$. The direct determination of the entropy contribution to the free energy from the reversible magnetization allows one to determine not only the correct values of the pinning energy, but also to extract quite detailed information on pancake vortex alignment. The characteristic field $H_{int} \sim {1/6} B_{\phi}$ at which intervortex repulsion begins to determine the vortex arrangement and the reversible magnetization is shown to coincide with a sharp increase in the irreversibility field $H_{irr}(T)$ and with the recoupling transition found in Josephson Plasma Resonance. Above $H_{int}$, the repulsive interaction between vortices cause both the vortex mobility to decrease and pancake alignement to increase. At higher fields $\gtrsim {1/3}B_{\phi}\gg B_{c1}$, free vortices outnumber those that are trapped on a columnar defect. This causes the decrease of c-axis resistivity and a second crossover of the irreversibility field, to a regime where it is determined by plastic creep., Comment: 12 Pages, 8 Figures

Using dynamic and thermodynamic magnetization measurements, we analyze the phase diagram of Bi_2Sr_2CaCu_2O_8delta single crystals containing amorphous columnar defects created by heavy-ion irradiation. Reversible magnetization experiments yield the respective magnitudes of the pinning energy and entropy contributions to the free energy of the vortex lattice. It appears that the entropy contribution in the London regime is relatively minor in both unirradiated and irradiated crystals, except in the case of high density of columns and inductions B that are smaller than the interaction field H_int ~ B_phi / 6. The dependence of the entropy contribution on vortex- and defect density correlates well with measurements of the irreversibility line H_irr, which shows a sharp increase at H_int., Comment: 8 pages, 6 figures; paper submitted to the first Euroconference of vortex matter under extreme conditions and scales ("VORTEX"); Agia Pelagia, Crete, September 18-24, 1999. For publication in Physica C

The penetration field H_p of Bi_2Sr_2CaCu_2O_{8+delta} crystals is determined from magnetization curves for different field sweep rates dH/dt and temperatures. The obtained results are consistent with theoretical reports in the literature about vortex creep over surface and geometrical barriers. The frequently observed low-temperature upturn of H_p is shown to be related to metastable configurations due to barriers for vortex entry. Data of the true lower critical field H_c1 are presented. The low-temperature dependence of H_c1 is consistent with a superconducting state with nodes in the gap function. [PACS numbers: 74.25.Bt, 74.60.Ec, 74.60.Ge, 74.72.Hs]