Constraints on the Quasiparticle Density of States in High-TcT_c Superconductors

In this Letter we present new tunneling data on YBa$_2$Cu$_3$O$_7$ thin films by low temperature scanning tunneling spectroscopy. Unusual peak-dip-hump features, previously reported in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, are also found in YBa$_2$Cu$_3$O$_7$. To analyse these common signatures we propose a new heuristic model in which, in addition to the d-wave symmetry, the gap function is energy dependent. A simple expression for the quasiparticle density of states is derived, giving an excellent agreement with the experiment. The dynamics of the quasiparticle states and the energy scales involved in the superconducting transition are discussed.Comment: 4 page Letter with 3 figure

Local tunneling spectroscopy of the electron-doped cuprate Sm1.85Ce0.15CuO4

We present local tunneling spectroscopy in the optimally electron-doped cuprate Sm2-xCexCuO4 x=0.15. A clear signature of the superconducting gap is observed with an amplitude ranging from place to place and from sample to sample (Delta~3.5-6meV). Another spectroscopic feature is simultaneously observed at high energy above \pm 50meV. Its energy scale and temperature evolution is found to be compatible with previous photoemission and optical experiments. If interpreted as the signature of antiferromagnetic order in the samples, these results could suggest the coexistence on the local scale of antiferromagnetism and superconductivity on the electron-doped side of cuprate superconductors

Two Gap State Density in MgB2_{2}: A True Bulk Property or A Proximity Effect?

We report on the temperature dependence of the quasiparticle density of states (DOS) in the simple binary compound MgB2 directly measured using scanning tunneling microscope (STM). To achieve high quality tunneling conditions, a small crystal of MgB2 is used as a tip in the STM experiment. The ``sample'' is chosen to be a 2H-NbSe2 single crystal presenting an atomically flat surface. At low temperature the tunneling conductance spectra show a gap at the Fermi energy followed by two well-pronounced conductance peaks on each side. They appear at voltages V$_{S}\simeq \pm 3.8$ mV and V$_{L}\simeq \pm 7.8$ mV. With rising temperature both peaks disappear at the Tc of the bulk MgB2, a behavior consistent with the model of two-gap superconductivity. The explanation of the double-peak structure in terms of a particular proximity effect is also discussed.Comment: 4 pages, 3 figure

Probing the superfluid velocity with a superconducting tip: the Doppler shift effect

We address the question of probing the supercurrents in superconducting (SC) samples on a local scale by performing Scanning Tunneling Spectroscopy (STS) experiments with a SC tip. In this configuration, we show that the tunneling conductance is highly sensitive to the Doppler shift term in the SC quasiparticle spectrum of the sample, thus allowing the local study of the superfluid velocity. Intrinsic screening currents, such as those surrounding the vortex cores in a type II SC in a magnetic field, are directly probed. With Nb tips, the STS mapping of the vortices, in single crystal 2H-NbSe_2, reveals both the vortex cores, on the scale of the SC coherence length $\xi$, and the supercurrents, on the scale of the London penetration length $\lambda$. A subtle interplay between the SC pair potential and the supercurrents at the vortex edge is observed. Our results open interesting prospects for the study of screening currents in any superconductor.Comment: 4 pages, 5 figure

Scanning Tunneling Spectroscopy on the novel superconductor CaC6

We present scanning tunneling microscopy and spectroscopy of the newly discovered superconductor CaC$_6$. The tunneling conductance spectra, measured between 3 K and 15 K, show a clear superconducting gap in the quasiparticle density of states. The gap function extracted from the spectra is in good agreement with the conventional BCS theory with $\Delta(0)$ = 1.6 $\pm$ 0.2 meV. The possibility of gap anisotropy and two-gap superconductivity is also discussed. In a magnetic field, direct imaging of the vortices allows to deduce a coherence length in the ab plane $\xi_{ab}\simeq$ 33 nm

Probing the superconducting condensate on a nanometer scale

Superconductivity is a rare example of a quantum system in which the wavefunction has a macroscopic quantum effect, due to the unique condensate of electron pairs. The amplitude of the wavefunction is directly related to the pair density, but both amplitude and phase enter the Josephson current : the coherent tunneling of pairs between superconductors. Very sensitive devices exploit the superconducting state, however properties of the {\it condensate} on the {\it local scale} are largely unknown, for instance, in unconventional high-T$_c$ cuprate, multiple gap, and gapless superconductors. The technique of choice would be Josephson STS, based on Scanning Tunneling Spectroscopy (STS), where the condensate is {\it directly} probed by measuring the local Josephson current (JC) between a superconducting tip and sample. However, Josephson STS is an experimental challenge since it requires stable superconducting tips, and tunneling conditions close to atomic contact. We demonstrate how these difficulties can be overcome and present the first spatial mapping of the JC on the nanometer scale. The case of an MgB$_2$ film, subject to a normal magnetic field, is considered.Comment: 7 pages, 6 figure

Nanometer Scale Mapping of the Density of States in an Inhomogeneous Superconductor

Using high speed scanning tunneling spectroscopy, we perform a full mapping of the quasiparticle density of states (DOS) in single crystals of BiPbSrCaCuO(2212). The measurements carried out at 5 K showed a complex spatial pattern of important variations of the local DOS on the nanometer scale. Superconducting areas are co-existing with regions of a smooth and larger gap-like DOS structure. The superconducting regions are found to have a minimum size of about 3 nm. The role of Pb-introduced substitutional disorder in the observed spatial variations of the local DOS is discussed.Comment: 4 page Letter with 3 figures (2 color figures

Pointwise consistency of the kriging predictor with known mean and covariance functions

This paper deals with several issues related to the pointwise consistency of the kriging predictor when the mean and the covariance functions are known. These questions are of general importance in the context of computer experiments. The analysis is based on the properties of approximations in reproducing kernel Hilbert spaces. We fix an erroneous claim of Yakowitz and Szidarovszky (J. Multivariate Analysis, 1985) that the kriging predictor is pointwise consistent for all continuous sample paths under some assumptions.Comment: Submitted to mODa9 (the Model-Oriented Data Analysis and Optimum Design Conference), 14th-19th June 2010, Bertinoro, Ital

Quasiparticle spectrum of the cuprate BiSrCaCuO: Possible connection to the phase diagram

We previously introduced [T. Cren et al., Europhys. Lett. 52, 203 (2000)] an energy-dependant gap function, $\Delta(E)$, that fits the unusual shape of the quasiparticle (QP) spectrum for both BiSrCaCuO and YBaCuO. A simple anti-resonance in $\Delta(E)$ accounts for the pronounced QP peaks in the density of states, at an energy $\Delta_p$, and the dip feature at a higher energy, $E_{dip}$. Here we go a step further : our gap function is consistent with the ($T, p$) phase diagram, where $p$ is the carrier density. For large QP energies ($E >> \Delta_p$), the total spectral gap is $\Delta(E) \simeq \Delta_p + \Delta_\phi$, where $\Delta_\phi$ is tied to the condensation energy. From the available data, a simple $p$-dependance of $\Delta_p$ and $\Delta_\phi$ is found, in particular $\Delta_\phi(p) \simeq 2.3 k_B T_c(p)$. These two distinct energy scales of the superconducting state are interpreted by comparing with the normal and pseudogap states. The various forms of the QP density of states, as well as the spectral function $A(k,E)$, are discussed

Nodal liquid and s-wave superconductivity in transition metal dichalcogenides

We explore the physical properties of a unified microscopic theory for the coexistence of superconductivity and charge density waves in two-dimensional transition metal dichalcogenides. In the case of particle-hole symmetry the elementary particles are Dirac fermions at the nodes of the charge density wave gap. When particle-hole symmetry is broken electron (hole) pockets are formed around the Fermi surface. The superconducting ground state emerges from the pairing of nodal quasi-particles mediated by acoustic phonons via a piezoelectric coupling. We calculate several properties in the s-wave superconducting phase, including specific heat, ultra-sound absorption, nuclear magnetic relaxation, thermal, and optical conductivities. In the case with particle-hole symmetry, the specific heat jump at the transition deviates strongly from ordinary superconductors. The nuclear magnetic response shows an anomalous anisotropy due to the broken time-reversal symmetry of the superconducting gap, induced by the triple charge density wave state. The loss of lattice inversion symmetry in the charge density wave phase leads to anomalous coherence factors in the optical conductivity and to the appearance of an absorption edge at the optical gap energy. Furthermore, optical and thermal conductivities display anomalous peaks in the infrared when particle-hole symmetry is broken.Comment: 23 pages, 16 figures. Published versio