Scanning Tunneling Spectroscopy in MgB2

We present scanning tunneling microscopy measurements of the surface of superconducting MgB2 with a critical temperature of 39K. In zero magnetic field the conductance spectra can be analyzed in terms of the standard BCS theory with a smearing parameter Gamma. The value of the superconducting gap is 5.2 meV at 4.2 K, with no experimentally significant variation across the surface of the sample. The temperature dependence of the gap follows the BCS form, fully consistent with phonon-mediated superconductivity in this novel superconductor. The application of a magnetic field induces strong pair-breaking as seen in the conductance spectra in fields up to 6 T.Comment: 4 pages, 4 figure

Predominantly Superconducting Origin of Large Energy Gaps in Underdoped Bi2Sr2CaCu2O8-d from Tunneling Spectroscopy

New tunneling data are reported in underdoped Bi2Sr2CaCu2O8-d using superconductor-insulator-superconductor break junctions. Energy gaps, Delta, of 51+2, 54+2 and 57+3 meV are observed for three crystals with Tc=77, 74, and 70 K respectively. These energy gaps are nearly three times larger than for overdoped crystals with similar Tc. Detailed examination of tunneling spectra over a wide doping range from underdoped to overdoped, including the Josephson IcRn product, indicate that these energy gaps are predominantly of superconducting origin.Comment: 10 pages, 4 figures, 1 tabl

Morita Equivalence, Picard Groupoids and Noncommutative Field Theories

In this article we review recent developments on Morita equivalence of star products and their Picard groups. We point out the relations between noncommutative field theories and deformed vector bundles which give the Morita equivalence bimodules.Comment: Latex2e, 10 pages. Conference Proceeding for the Sendai Meeting 2002. Some typos fixe

Coherent quasiparticle weight and its connection to high-T_c superconductivity from angle-resolved photoemission

In conventional superconductors, the pairing energy gap (\Delta) and superconducting phase coherence go hand-in-hand. As the temperature is lowered, both the energy gap and phase coherence appear at the transition temperature T_c. In contrast, in underdoped high-T_c superconductors (HTSCs), a pseudogap appears at a much higher temperature T^*, smoothly evolving into the superconducting gap at T_c. Phase coherence on the other hand is only established at T_c, signaled by the appearance of a sharp quasiparticle (QP) peak in the excitation spectrum. Another important difference between the two types of superconductors is in the ratio of 2\Delta / T_c=R. In BCS theory, R~3.5, is constant. In the HTSCs this ratio varies widely, continuing to increase in the underdoped region, where the gap increases while T_c decreases. Here we report that in HTSCs it is the ratio z_A\Delta_m/T_c which is approximately constant, where \Delta_m is the maximum value of the d-wave gap, and z_A is the weight of the coherent excitations in the spectral function. This is highly unusual, since in nearly all phase transitions, T_c is determined by an energy scale alone. We further show that in the low-temperature limit, z_{\it A} increases monotonically with increasing doping x. The growth is linear, i.e. z_A(x)\propto x, in the underdoped to optimally doped regimes, and slows down in overdoped samples. The reduction of z_A with increasing temperature resembles that of the c-axis superfluid density.Comment: 11 pages, 5 figures, revised versio

C-axis electronic Raman scattering in Bi_2Sr_2CaCu_2O_{8+\delta}

We report a c-axis-polarized electronic Raman scattering study of Bi_2Sr_2CaCu_2O_{8+\delta} single crystals. In the normal state, a resonant electronic continuum extends to 1.5 eV and gains significant intensity as the incoming photon energy increases. In the superconducting state, a coherence 2\Delta peak appears around 50 meV, with a suppression of the scattering intensity at frequencies below the peak position. The peak energy, which is higher than that seen with in-plane polarizations, signifies distinctly different dynamics of quasiparticle excitations created with out-of-plane polarization.Comment: 12 pages, REVTEX, 3 postscript figure

Nesting properties and anisotropy of the Fermi surface of LuNi2_{2}B2_{2}C

The rare earth nickel borocarbides, with the generic formula $R$Ni$_{2}$B$_{2}$C, have recently been shown to display a rich variety of phenomena. Most striking has been the competition between, and even coexistence of, antiferromagnetism and superconductivity. We have measured the Fermi surface (FS) of LuNi$_{2}$B$_{2}$C, and shown that it possesses nesting features capable of explaining some of the phenomena experimentally observed. In particular, it had previously been conjectured that a particular sheet of FS is responsible for the modulated magnetic structures manifest in some of the series. We report the first direct experimental observation of this sheet.Comment: 4 pages, 4 PS figure

Scanning tunneling spectroscopy of high-temperature superconductors

Tunneling spectroscopy played a central role in the experimental verification of the microscopic theory of superconductivity in the classical superconductors. Initial attempts to apply the same approach to high-temperature superconductors were hampered by various problems related to the complexity of these materials. The use of scanning tunneling microscopy/spectroscopy (STM/STS) on these compounds allowed to overcome the main difficulties. This success motivated a rapidly growing scientific community to apply this technique to high-temperature superconductors. This paper reviews the experimental highlights obtained over the last decade. We first recall the crucial efforts to gain control over the technique and to obtain reproducible results. We then discuss how the STM/STS technique has contributed to the study of some of the most unusual and remarkable properties of high-temperature superconductors: the unusual large gap values and the absence of scaling with the critical temperature; the pseudogap and its relation to superconductivity; the unprecedented small size of the vortex cores and its influence on vortex matter; the unexpected electronic properties of the vortex cores; the combination of atomic resolution and spectroscopy leading to the observation of periodic local density of states modulations in the superconducting and pseudogap states, and in the vortex cores.Comment: To appear in RMP; 65 pages, 62 figure

Multiple Deprivation, Severity and Latent Sub-Groups:Advantages of Factor Mixture Modelling for Analysing Material Deprivation

Material deprivation is represented in different forms and manifestations. Two individuals with the same deprivation score (i.e. number of deprivations), for instance, are likely to be unable to afford or access entirely or partially different sets of goods and services, while one individual may fail to purchase clothes and consumer durables and another one may lack access to healthcare and be deprived of adequate housing . As such, the number of possible patterns or combinations of multiple deprivation become increasingly complex for a higher number of indicators. Given this difficulty, there is interest in poverty research in understanding multiple deprivation, as this analysis might lead to the identification of meaningful population sub-groups that could be the subjects of specific policies. This article applies a factor mixture model (FMM) to a real dataset and discusses its conceptual and empirical advantages and disadvantages with respect to other methods that have been used in poverty research . The exercise suggests that FMM is based on more sensible assumptions (i.e. deprivation covary within each class), provides valuable information with which to understand multiple deprivation and is useful to understand severity of deprivation and the additive properties of deprivation indicators

Pinned Balseiro-Falicov Model of Tunneling and Photoemission in the Cuprates

The smooth evolution of the tunneling gap of Bi_2Sr_2CaCu_2O_8 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 (pi,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 T_c, the sharp peak at Delta_1 and the dip seen in the tunneling and photoemission near 2Delta_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.Comment: 18 pages LaTeX, 26 ps. figure