Session D13: STS and Imaging of Superconductors

Imaging studies of hole-electron asymmetry observed in a lightly-doped high-$T_{\rm c}$ superconductor Ca$_{2-x}$Na$_x$CuO$_2$Cl$_2$

We have reported spectroscopic imaging on the electronic state intervening between the Mott insulator and the $d$-wave superconductor [1]. The electronic state with $|E|<100$~meV shows complex spatial modulations with $4a_0\times 4a_0$ ($a_0$: in-plane lattice constant) correlations. Moreover, the tunneling spectra show characteristic hole-electron asymmetry, which is thought to be related to the approach of the Mott insulator [2]. Here we report on new studies of imaging the 'Mottness' through mapping the asymmetry in tunneling spectra associated with high energies $|E|>100$~meV. Spectroscopic mapping of the asymmetry reveals strong $4a_0\times 4a_0$ periodic modulation up to several hundreds meV. However the $4a_0/3\times 4a_0/3$ component, which appears in the Fourier transform of the checkerboard pattern observed at $|E|<100$~meV, is negligle. This spatial modulation of the 'Mottness' may indicate that hole density is modulated with the $4a_0\times 4a_0$ periodicity. This would imply that the $4a_0/3\times 4a_0/3$ periodicity observed at lower energies may arise from umklapp scattering due to the hole density modulation. [1] T. Hanaguri {\it et al}., Nature 430, 1001 (2004). [2] P. W. Anderson and N. P. Ong, cond-mat/0405518.   

Investigation of Competing Orders and Quantum Criticality in Cuprate Superconductors using Scanning Tunneling Microscopy

The existence of competing orders in cuprate superconductors and their proximity to quantum criticality give rise to a variety of non-universal phenomena. To investigate this issue, we study the quasi-particle tunneling spectra of various cuprates with a low- temperature scanning tunneling microscope. Specifically, we will present the temperature evolution and the spatial variation of the quasi-particle tunneling spectra of the \emph{s}-wave pairing electron-doped infinite-layer $Sr_{0.9}La_{0.1}CuO_2$ and the \emph{d}-wave pairing optimally hole-doped $YBa_2Cu_3O_x$. We will compare the spectroscopy with bulk magnetic measurements as a function of applied field and discuss the physics implication.   

A flow-through SQUID microscope for NDE of defects in superconducting wires

An integral component of MRI superconducting magnets is the LTS wire used to generate the magnetic field. These magnets are wound from km-long sections, and a single defect can adversely affect its performance. We have modified the nose cone of our high-Tc cryocooled SQUID microscope to enable fast NDE of long wires. A thin tube is positioned immediately beneath the SQUID chip, while a motor-controlled feed mechanism pulls the wire through the tube. We describe the design and operation of the flow-through system, and present measurement results.   

Scanning SQUID microscopy of SFS $\pi$-Josephson junction arrays

We use a Scanning SQUID Microscope to image the magnetic flux distribution in arrays of SFS (superconductor-ferromagnet-superconductor) Josephson junctions. The junctions are fabricated with barrier thickness such that they undergo a transition to a $\pi $-junction state at a temperature T$_{\pi } \quad \approx $ 2-4 K. In arrays with cells that have an odd number of $\pi $-junctions, we observe spontaneously generated magnetic flux in zero applied magnetic field. We image both fully-frustrated arrays and arrays with non-uniform frustration created by varying the number of $\pi $-junctions in the cells. By monitoring the onset of spontaneous flux as a function of temperature near T$_{\pi }$,$^{ }$we estimate the uniformity of the junction critical currents.   

Evolution of Low-Energy Andreev States under an Applied Supercurrent in YBa$_2$Cu$_3$O$_{7-\delta}$

We present scanning tunneling spectroscopy measurements on current-carrying YBa$_2$Cu$_3$O$_{7-\delta}$ thin-film strips at 4.2K, showing the evolution of the phase-sensitive low-energy Andreev states. In the low-current regime, well below the Landau depairing limit, the Andreev states are anomalously suppressed, suggesting nanoscale dephasing of the \emph{d}-wave order parameter. Measurements are also made at higher applied current levels to probe possible \emph{local} chiral states in the pairing symmetry. These results will be discussed in the context of order parameter non-rigidity in the high-$T_c$ cuprates.   

Interplay of quantum size effects, electron-phonon interactions, and superconductivities in ultra-thin Pb films on Si(111) - An STM/S study

We report a LT-STM study of quantum size effect upon the superconductivity in ultra-thin Pb films on Si(111). Ultra-thin Pb films (10 -- 30 ML) on Si(111) were grown with two different methods: (a) room temperature deposition leading to a morphology of separated 2D islands; and (b) low temperature deposition followed by room temperature annealing leading to a uniformly covered film. A home-built STM with the operation temperature ranging from 2.5 K to 300K is used to study the electronic properties. The local thickness of the Pb film is directly determined by probing the quantum well states (QWS). Clear superconducting gap was observed on the Pb film at low temperature ($<$ 5.5 K) and disappeared at higher temperature (e.g. 8.7 K). Temperature dependence study allows us to determine the T$_{c}$ unambiguously. In addition to the superconducting gap, we observed pronounced phonon-related features. Interestingly, these phonon-related features show spatial modulation even on the film of uniform thickness. On the other hand, the superconducting gap depends primarily on the layer thickness. More detailed analysis of the interplay of quantum size effects, electron-phonon interactions, and superconductivities will be reported.   

High frequency scanning SQUID microscope

One important application of scanning SQUID microscopes is to fault detection in integrated circuits and multi-chip modules. However, the present generation of computer processors operate at over 1 GHz, well above the bandwidth of the present generation of SQUID microscopes. We present results for a 4.2 K scanning SQUID microscope with a bandwidth in the GHz range. We have overcome the bandwidth limitations of traditional scanning SQUID microscopes by removing the main bandwidth limiter – the conventional flux-locked loop electronics - and using instead a pulsed sampling technique with a hysteretic SQUID. We describe the overall design and operation of our system, and present high-speed measurement results.   

Direct observation of single-electron tunneling oscillations

We report real time detection of time correlated single-electron tunneling oscillations in a series array of small tunnel junctions$^1$. Here the current, $I$, is made up of a lattice of charge solitons moving throughout the array by time correlated tunneling with frequency $f=I/e$, where $e$ is the electron charge. This phenomenon is analogous to the a.c.\ Josephson effect, but not fully dual since the oscillations are not coherent. To detect the single electrons, we have integrated the array with an RF-SET and injected the full charge into the SET island. In this fundamentally new way we have measured extremely small currents$^2$, ranging from 5 fA to 1 pA by counting single electrons. Our results suggest that very good accuracy can be achieved in the future. Since current is related to frequency by a natural constant only, the measurement is self calibrated and does not suffer from offset or drift; it also opens a possibility to realize the quantum metrological triangle.\\~\\ $^1$E. Ben-Jacob, Y. Gefen, Phys. Lett. A 108A, 289 (1985)\\ D.V. Averin, K.K. Likharev, J. Low Temp. Phys. 62, 345 (1986)\\ $^2$J. Bylander, T. Duty, P. Delsing, cond-mat/0411420   

Characterization of Zn impurity resonances in strongly underdoped Bi-2212

Using atomically resolved scanning tunneling spectroscopy (STS), we investigate the local density of states (LDOS) in the vicinity of Zn impurity atoms in strongly underdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$. Previous studies have shown a correlation between the local superconducting energy gap and the locations of these impurities (Lang \textit{et al,} \textit{Nature,} 415, 2002; McElroy \textit{et al,} cond-mat/040620). Different classes of scattering resonance are observed, and we present the results of preliminary experiments to characterize them and determine their relationship to the local electronic structure found in the underdoped samples.   

Study of Defect Scattering in the Pseudogap State of $Bi_2Sr_2CaCu_2O_{8+\delta}$

The pseudogap state in high-Tc superconductors continues to be one of the most puzzling aspects of these materials. The local response of this unusual electronic state to defects can potentially teach us about its underlying electronic correlations. Using a home-built scanning tunneling microscope (STM) we have performed spatially resolved measurements of the density of states in Ni and Zn doped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ samples in the pseudogap state above Tc. We will present these measurements and compare them to similar studies in the superconducting state.   

Fourier Transform Inelastic Electron Tunneling Spectroscopy: A new tool for exploration of electron-boson interactions in High-Tc superconductors

Since the early works, Inelastic Electron Tunneling Spectroscopy(IETS) has been the most sensitive tool to probe collective modes in the solid state. McMillan/Rowell utilized this technique to elucidate the phonon structures in the conventional superconductors, and Stipe et al. succeeded in IETS using low temperature STM(LT-STM). So far none of these works had momentum space resolution. Recently, McElroy et al. introduced the Fourier Transform Scanning Tunneling Spectroscopy(FT-STS) technique to get k-space information about quasi-particles in the high-Tc Superconductors using LT-STM. Here we report developement of the FT-IETS technique, on the basis of the previous works above, for the study of the high-Tc. This technique has the potential to be a powerful tool for probing local characteristic, as well as the momentum space information of the bosonic modes in the high-Tc superconductors. We will also present some preliminary results from this technique on Bi-2212.   

Proximity Effect in Gold-Coated YBa$_2$Cu$_3$O$_{7-\delta}$ Films Studied by Scanning Tunneling Spectroscopy

Scanning tunneling microscopy and spectroscopy measurements were performed on proximity systems of the high temperature superconductor YBa$_{2}$Cu$_{3}$O$_{7-\delta }$ (YBCO) covered by a normal gold layer of various thicknesses. Tunneling spectroscopy of gold layers overcoating $c$-axis YBCO films reveals proximity-induced gap structures. The gap size reduces exponentially with the distance from $a$-axis facets, indicating that the proximity effect is primarily due to the (100) YBCO facets. The normal penetration depth, $\xi _{n,}$ is in agreement with estimations for a dirty limit proximity system[1]. The proximity effect changes considerably for (110)YBCO/Au bilayers. While proximity-induced mini-gaps rarely appear in the Au layer, the Andreev bound states, clearly penetrate into the metal. Zero bias conductance peaks are measured on Au layers thinner than 7 nm with a magnitude similar to those detected on the bare superconductor films. The peaks then decay abruptly with Au thickness and disappear above 10 nm. This length is shorter than the normal coherence length and corresponds to the (ballistic) mean free path[2]. $^{1}$Sharoni A. \textit{et al.} Phys. Rev. Lett. \textbf{92} 017003 (2004). $^{2}$Asulin I. \textit{et al.} Phys. Rev. Lett. \textbf{93}, 157001 (2004).   

Magnetic Imaging of Transport Current Distributions in Coated Conductors Using an Improved Inversion Algorithm

Magnetic imaging may be used to study and optimize transport current in superconducting YBa$_{2}$Cu$_{3}$O$_{7-\delta }$ coated conductors. We magnetically image transport currents in order to identify regions of good and poor superconductor. The internal current distribution can be derived from the external magnetic fields using the Biot-Savart law. The fastest method, especially for dense images, has the limitation of introducing errors on the order of 20{\%} when the imaging area is only little larger than the conductor, a common experimental constraint, and when transport currents enter and exit the imaging area. We have developed a fast inversion procedure that works on tape samples under transport current with an accuracy of 1{\%} or better. The algorithm is ideally suited for high resolution and high throughput characterizations. In addition, we will discuss a variation of this technique, which serves to reduce the effects of measurement errors in the computed current distributions due to imperfections of magnetoresistive sensors. Through this technique the source of the reduced critical current in a commercially manufactured tape was deduced.   

VTSLM reveals Current Distribution around Features in Striated YBCO

Variable Temperature Scanning Laser Microscopy (VTSLM) has revealed current bottlenecks in striated superconducting tapes. Our goal is to check the current distribution and see if the striations play a role. Each sample is first given a steady current and varied temperature to determine its transition temperature (for YBCO, usually 90K +/- 4K). Since the transition temperature has a dramatic change in resistance (from normal metal to superconductor in span of 1K), local heating with the scanning laser evokes measurable voltage change. We scanned the laser back and forth across the sample taking smaller and smaller steps to increase resolution. After six samples (three each of a particular geometry) were tested, current patterns emerged. Current bottlenecks, or greater current density due to physical features of sample, are evident in the following locations: near gaps in striations, near visible features in material (blemish or scratch), and where two or more channels merge into one channel (due to blocked channel.) We conclude that the current bottlenecks are the main causes for reducing the current carrying capability in striated YBCO samples.   

A New Electrometer based on Quantum Capacitance

We propose a new kind of electrometer that exploits the parametric quantum capacitance (C$_{Q})$ of a single cooper-pair box (SCB). The C$_{Q}$ is the curvature of the ground-state energy band. Near the charge degeneracy point, the curvature arises from the avoided level crossing induced by the Josephson coupling. The C$_{Q}$ depends strongly on gate charge and can be larger than the geometric capacitance. The designs embeds a SCB in a resonant circuit and detects changes in the C$_{Q}$ as changes in the phase of a reflected microwave signal. The device is similar to an RF-SET, but has potential advantages. (Our group has recently measured the C$_{Q}$ of an RF-SET.) In the standard RF-SET, a dissipative bias current must be passed from source to drain. This current is the source of significant backaction at the mesoscopic scale. The C$_{Q}$ electrometer has no bias current nor intrinsic dissipation. Therefore, its noise temperature should approach the standard quantum limit. Semiclassical calculations confirm this and predict the charge sensitivity should be comparable to the RF-SET. This approach is dual to recent proposals exploiting the Josephson inductance.