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

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

Spectroscopic evidence for strong correlations between local superconducting gap and local Altshuler-Aronov density-of-states suppression in ultrathin NbN films

Disorder has different profound effects on superconducting thin films. For a large variety of materials, increasing disorder reduces electronic screening which enhances electron-electron repulsion. These fermionic effects lead to a mechanism described by Finkelstein: when disorder combined to electron-electron interactions increases, there is a global decrease of the superconducting energy gap $\Delta$ and of the critical temperature $T_c$, the ratio $\Delta$/$k_BT_c$ remaining roughly constant. In addition, in most films an emergent granularity develops with increasing disorder and results in the formation of inhomogeneous superconducting puddles. These gap inhomogeneities are usually accompanied by the development of bosonic features: a pseudogap develops above the critical temperature $T_c$ and the energy gap $\Delta$ starts decoupling from $T_c$. Thus the mechanism(s) driving the appearance of these gap inhomogeneities could result from a complicated interplay between fermionic and bosonic effects. By studying the local electronic properties of a NbN film with scanning tunneling spectroscopy (STS) we show that the inhomogeneous spatial distribution of $\Delta$ is locally strongly correlated to a large depletion in the local density of states (LDOS) around the Fermi level, associated to the Altshuler-Aronov effect induced by strong electronic interactions. By modelling quantitatively the measured LDOS suppression, we show that the latter can be interpreted as local variations of the film resistivity. This local change in resistivity leads to a local variation of $\Delta$ through a local Finkelstein mechanism. Our analysis furnishes a purely fermionic scenario explaining quantitatively the emergent superconducting inhomogeneities, while the precise origin of the latter remained unclear up to now.Comment: 11 pages, 4 figure

Confinement of superconducting fluctuations due to emergent electronic inhomogeneities

The microscopic nature of an insulating state in the vicinity of a superconducting state, in the presence of disorder, is a hotly debated question. While the simplest scenario proposes that Coulomb interactions destroy the Cooper pairs at the transition, leading to localization of single electrons, an alternate possibility supported by experimental observations suggests that Cooper pairs instead directly localize. The question of the homogeneity, granularity, or possibly glassiness of the material on the verge of this transition is intimately related to this fundamental issue. Here, by combining macroscopic and nano-scale studies of superconducting ultrathin NbN films, we reveal nanoscopic electronic inhomogeneities that emerge when the film thickness is reduced. In addition, while thicker films display a purely two-dimensional behaviour in the superconducting fluctuations, we demonstrate a zero-dimensional regime for the thinner samples precisely on the scale of the inhomogeneities. Such behavior is somehow intermediate between the Fermi and Bose insulator paradigms and calls for further investigation to understand the way Cooper pairs continuously evolve from a bound state of fermionic objects into localized bosonic entities.Comment: 29 pages 9 figure

Imaging the essential role of spin-fluctuations in high-Tc superconductivity

We have used scanning tunneling spectroscopy to investigate short-length electronic correlations in three-layer Bi2Sr2Ca2Cu3O(10+d) (Bi-2223). We show that the superconducting gap and the energy Omega_dip, defined as the difference between the dip minimum and the gap, are both modulated in space following the lattice superstructure, and are locally anti-correlated. Based on fits of our data to a microscopic strong-coupling model we show that Omega_dip is an accurate measure of the collective mode energy in Bi-2223. We conclude that the collective mode responsible for the dip is a local excitation with a doping dependent energy, and is most likely the (pi,pi) spin resonance.Comment: 4 pages, 4 figure

Fluctuation Dominated Josephson Tunneling with a Scanning Tunneling Microscope

We demonstrate Josephson tunneling in vacuum tunnel junctions formed between a superconducting scanning tunneling microscope tip and a Pb film, for junction resistances in the range 50-300 k$\Omega$. We show that the superconducting phase dynamics is dominated by thermal fluctuations, and that the Josephson current appears as a peak centered at small finite voltages. In the presence of microwave fields (f=15.0 GHz) the peak decreases in magnitude and shifts to higher voltages with increasing rf power, in agreement with theory.Comment: 4 pages, REVTeX, submitted to PR

Continuous loading of a non-dissipative atom trap

We study theoretically a scheme in which particles from an incident beam are trapped in a potential well when colliding with particles already present in the well. The balance between the arrival of new particles and the evaporation of particles from the trapped cloud leads to a steady-state that we characterize in terms of particle number and temperature. For a cigar shaped potential, different longitudinal and transverse evaporation thresholds can be chosen. We show that a resonance occur when the transverse evaporation threshold coincides with the energy of the incident particles. It leads to a dramatic increase in phase space density with respect to the incident beam.Comment: 7 pages, 2 figure

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

Interlayer tunneling spectroscopy of Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta}: a look from inside on the doping phase diagram of high TcT_c superconductors

A systematic, doping dependent interlayer tunneling spectroscopy of Bi2212 high $T_c$ superconductor is presented. An improved resolution made it possible to simultaneously trace the superconducting gap (SG) and the normal state pseudo-gap (PG) in a close vicinity of $T_c$ and to analyze closing of the PG at $T^*$. The obtained doping phase diagram exhibits a critical doping point for appearance of the PG and a characteristic crossing of the SG and the PG close to the optimal doping. This points towards coexistence of two different and competing order parameters in Bi2212. Experimental data indicate that the SG can form a combined (large) gap with the PG at $T<T_c$ and that the interlayer tunneling becomes progressively incoherent with decreasing doping.Comment: 5 pages, 5 figure