Session A10: Tunneling on Cuprate Superconductors

Local tunneling probe of low-energy Andreev states on (110) Y$_{0.95}$Ca$_{0.05}$Ba$_2$Cu$_3$O$_{7-\delta}$ thin films in an applied magnetic field

Cryomagnetic scanning tunneling spectroscopy (STS) was performed on (110)-oriented Y$_{0.95}$Ca$_{0.05}$Ba$_2$Cu$_3$O$_ {7-\delta}$ thin films, in order to reveal coherence-length scale information on the symmetry of the high-$T_c$ order parameter (OP) in a magnetic field. In zero-field at 4.2K, both spontaneously split and unsplit zero-bias conductance peaks (ZBCP) are seen in the STS spectrum. The two types of peak spectra exhibit increasing splitting in a field applied along the $c$-axis of the film. Both spontaneous and field-induced ZBCP splitting indicate a lifting in the degeneracy of the low- energy Andreev states, consistent with time-reversal symmetry breaking. These results are discussed within the context of the Doppler effect as well as intrinsic \emph{vs.} field-induced complex components in the high-$T_c$ OP.   

Magnetic-field effect on the quasiparticle excitation observed by the tunneling spectroscopy in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ single crystal

In the $d$-wave superconductor, due to the existence of nodes of the pairing gap, the field-dependence of the quasiparticle density of state has been predicted to be essentially different from the behavior in the $s$-wave case [1]. Here we report the planar junction tunneling spectra at different magnetic fields in the high-$T_{c}$ superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ to study how the field modifies the quasiparticle excitation. [1] G. E. Volovik, JETP Lett. \textbf{58}, 469 (1993).   

Role of competing orders (COs) in the low-energy pseudogap (PG) phenomena and quasiparticle (QP) excitations of hole- and electron-type cuprate superconductors

Our cryogenic scanning tunneling spectroscopic studies of spatially resolved QP density of states (DOS) in hole-type YBa$_{2}$Cu$_{3}$O$_{x}$ and electron-type La$_{0.1}$Sr$_{0.9}$CuO$_{2}$ cuprate superconductors (SC) reveal that the existence of COs in the cuprates can account for many seeming non-universal phenomena. Namely, we analyze the low-energy QP excitation spectra by using a microscopic model of coexisting SC/CO, with density-wave type COs, and find that various spectral characteristics are uniquely determined by the parameters $\Delta _{SC}$, V$_{CO}$, Q, $\eta $, and $\Gamma $ ($\Delta _{SC}$: SC gap, V$_{CO}$: CO gap, Q: CO wave-vector, $\eta $: strength of quantum fluctuations, $\Gamma $: line-width of QP spectral peak). For instance, V$_{CO}>\Delta _{SC}$ (V$_{CO}$\underline {$<$}$\Delta _{SC})$ in hole- (electron-) type cuprates can account for the presence (absence) of the low-energy PG. Anomalous momentum-dependent QP properties such as the Fermi arcs and antiferromagnetic hot spots can also be explained. In finite magnetic fields, the QP DOS inside the vortex core of both types of cuprates reveal unconventional PG-like features at energies comparable to the V$_{CO}$ values derived by our analysis.   

Spatially Resolved Quasiparticle (QP) Spectra in the Vortex State of Electron-Type Cuprate Superconductor (SC) La$_{0.1}$Sr$_{0.9}$CuO$_{2}$(La-112)

The low-energy excitations of cuprate superconductors are unconventional and are susceptible to changes in temperature, doping and magnetic field. Our recent experiments and microscopic theoretical analysis suggest that these phenomena may be attributed to the presence of competing orders (COs) and strong quantum fluctuations. Here we present our scanning tunneling spectroscopic studies that support coexisting SC/CO in La-112, an optimally-doped electron-type cuprate with $T_{c}$=43 K. In zero-field, the histogram of the QP spectra at 9 K over an (100$\times $100) nm$^{2}$ area reveals a single set of spatially homogeneous peaks at $\Delta _{eff}$ = 11.8$\pm $1.5 meV. Our analysis of the data (with two energy gaps of SC and CO, $\Delta _{SC}$ and V$_{CO})$ suggests $\Delta _{eff}$ = [($\Delta _{SC})^{2}$+(V$_{CO})^{2}$]$^{1/2}$, $\Delta _{SC}>$V$_{CO}$, and the presence of quantum fluctuations. With increasing magnetic field to 6 Tesla, $\Delta _{eff}$ shifts downward to 10.0 meV due to the overall suppression of $\Delta _{SC}$, and the spatial variation of the spectra are consistent with vortex periodicity. Moreover, pseudogap-like spectral features occur at $\sim \pm $V$_{CO}$ inside the vortex cores while the spectra outside the vortex cores retain a gap value at $\sim \pm \Delta _{eff}$. This work was supported by NSF Grant DMR-0405088.   

Importance of matrix element effects in the scanning tunneling spectra of $Bi_2Sr_2CaCu_2O_{8+\delta}$

Scanning tunneling microscopy/spectroscopy (STM/STS) techniques have entered the realm of high-Tc's impressively by offering atomic scale real space resolution and meV resolution in bias voltages. STM/STS spectra, however, represent a complex mapping of electronic states of interest related to the CuO2 planes, since the tunneling current must reach the tip after being filtered through the overlayers (e.g. SrO and BiO in Bi2212). We have developed a Green function approach for realistic modeling of STM/STS spectra of the cuprates, where the tunneling current is evaluated directly including the effect of overlayers, with all orbitals within a few eV's of the Fermi energy $E_F$ accounted for. Our computations show the presence of strong matrix element effects, which lead to significant differences between the dI/dV spectra and the local density of states (LDOS) of CuO2 planes. For instance, the $d_{x^2-y^2}$ signal is found to be dominated by non-vertical hopping between the CuO$_2$ and BiO layers. A substantial electron-hole anisotropy of the tunneling spectrum, which is in accord with experiments, is naturally explained by the contribution from $d_ {z^2}$ and other orbitals below $E_F$.   

Temperature dependent Scanning Tunneling Spectroscopy of impurities in Bi2Sr2CuO6+x through the transition temperature

Scanning Tunneling Microscopy has been used to study detailed electronic spectrum in atomic scale defects in high temperature superconductors. We present Scanning Tunneling Spectroscopy of impurities in Bi$_{2}$Sr$_{2}$CuO$_{6+x }$(Bi-2201) over a wide range of temperatures. Surprisingly, native impurity resonances, similar to the ones previously observed in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ (Bi-2212), spatially coexist with the superconducting gap at low temperatures and survive almost unchanged through the superconducting transition temperature T$_{c}$. We shall discuss the implications of these findings on the relationship between superconducting gap and pseudogap in these materials.   

Visualizing Two Gaps in the High Temperature Superconductor Bi-2201

The relationship between the superconducting and pseudogap states in the cuprates has been a subject of much interest as well as debate in the HTS community. At the forefront of this debate is whether the pseudogap exists below Tc, and if it does, in what capacity. We present scanning tunneling microscopy measurements which provide evidence for two distinct but simultaneously coexisting gaps in the density of states of Bi2Sr2CuO6+x (Bi-2201) below Tc; one identified as the superconducting gap and the other, the pseudogap. In addition, we discuss our preliminary doping dependence measurements showing that the small (superconducting) gap scales with Tc while the larger (pseudogap) gap scales with T* indicating a consistency with their identification.   

Temperature and doping dependent FT-STS studies of Bi-2201

We present Fourier transform scanning tunneling spectroscopy (FT-STS) results in superconducting Bi-2201. The data presented are drawn from samples at a variety of dopings, and from experiments both below and above the superconducting transition temperature T$_{c}$. A number of unexpected trends are revealed by this systematic study. We interpret the results in light of several theories and make comparisons to results from other crystal systems.   

Bogoliubov angle and visualization of particle-hole mixture in superconductors.

We propose a new technique to visualize particle-hole mixture in high temperature superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$, using the Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM). Depending on the polarity of bias voltage, SI-STM can sample the particle and hole content of a superconducting excitation, Bogoliubov quasiparticle. `Bogoliubov angle' (BA) is a measure of the relative weight of particle and hole amplitude in the Bogoliubov quasiparticle, which is determined by taking ratio of the differential conductance at positive and negative biases. BA allows one to measure directly the energy and position dependent particle-hole admixture and therefore visualize robustness of superconducting state locally. We will demonstrate the power of this new technique and discuss the momentum space (q-space) electronic structure in the talk.   

Phase-sensitive scattering of Bogoliubov quasi-particles in (Ca,Na)$_2$CuO$_2$Cl$_2$ under magnetic field

Magnetic-field effect on the quasi-particle interference (QPI) in Ca$_{1.86}$Na$_{0.14}$CuO$_2$Cl$_2$ ($T_{\rm c} \sim 28$~K) has been studied using Fourier-transform spectroscopic-imaging scanning tunneling microscopy. In the absence of magnetic field, all scattering vectors expected from the octet model for QPI [1] were detected in the Fourier-transformed conductance-ratio maps [2]. We have found that magnetic field enhances (suppresses) the amplitude of the standing waves due to QPI if the signs of the $d$-wave superconducting order parameter in momentum space are the same (different) between initial and final states of the scatterings. Such sensitivity to the phase of the order parameter indicates that coherence factors play an important role. \newline [1] K. McElroy {\it et al.}, Nature {\bf 422}, 592 (2003). \newline [2] T. Hanaguri {\it et al.}, Nature Phys. published online/nphys753.   

Evolution of the electronic excitation spectrum with strongly diminishing hole-density in superconducting Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$

We use tunneling spectroscopy to measure the T$>$0 spectrum of electronic excitations N(E) over a wide range of hole-density in superconducting Bi2212. We introduce a parameterization for N(E) based an anisotropic d-wave energy-gap plus an effective scattering rate which varies linearly with energy. We demonstrate that this form of N(E) allows successful fitting of differential tunnelling conductance spectra throughout much of the Bi2212 phase diagram. A single, particle-hole symmetric, anisotropic energy-gap, in combination with a strongly energy dependent effective scattering rate, can describe the excitations without recourse to an additional energy gap of another ordered state. However we also observe two distinct and diverging energy scales in the system: the energy-gap maximum $\Delta _{1}$ and a lower energy scale $\Delta _{0}$ separating the spatially homogeneous and heterogeneous electronic structures.   

Temperature Evolution of Local Pairing {\&} Electron-Boson Coupling in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$

Recently, we have shown using variable temperature scanning tunneling microscopy measurements that the pairing in high-Tc superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ persists in nanoscale regions at temperatures above Tc. [1] Using the ability to track the same atomic location with temperature, we have examined the evolution of the electronic states from well below Tc to above the temperature at which the pairs first form locally. We will present these results for an overdoped sample. Using these measurements we extract the evolution of the pairing gap with temperature and show that pairing gaps at different atomic sites close at different temperatures. Our technique also allows us to quantitatively analyze the local electron-boson coupling for different atomic sites with different pairing strengths. Our results show that there is no connection between the variation of the gap magnitude and the bosonic mode associated with the ``dip-hump'' feature in the spectra. [1] Gomes et al. Nature 447, 569--572 (2007).   

Electronic Origin of the Nanoscale Variation of Pairing Gaps in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$

The magnitude of the low-temperature superconducting gap measured in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ shows large nanoscale spatial variations. On raising the temperature, these superconducting gaps disappear locally at temperatures above the superconducting transition temperature Tc. We present the first atomically resolved measurements of the spectrum of overdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ at temperatures where all gaps have closed. We show that the shape of this ``normal'' state spectrum is inhomogeneous over a length scale similar to that of the gap variation at low temperature. We then track the same lattice sites down to low temperature and observe the opening of gaps in the spectrum. We will discuss the relationship between the shape of the spectrum measured in the ``normal'' state at high temperature and the size of the low-temperature superconducting gap at the same atomic site.   

Temperature Evolution of the Electronic States {\&} Multiple Gap Features in Bi$_{2}$Sr$_{2-y}$La$_{y}$CuO$_{6}$.

Like Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$, Bi$_{2}$Sr$_{2-y}$La$_{y}$CuO$_{6 }$samples show inhomogeneous gaps in the DOS at low temperature. We present atomic resolution STM spectroscopy measurements of the evolution of the DOS with temperature for optimal (y=0.4) and overdoped (y$<$0.4) samples and compare these measurements to Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$. In Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$, the low temperature (T$<$Tc) spectra of overdoped samples are all characterized by a single d-wave gap with sharp coherence peaks. In contrast, Bi$_{2}$Sr$_{2-y}$La$_{y}$CuO$_{6 }$shows a variety of spectra at low temperature ranging from those without gaps to ones with multiple gap features [1]. By measuring the temperature evolution of these gap features at given lattice sites for various doping levels, we estimate the local temperature at which pairing develops in these samples. [1] Boyer et al., Nat Phys 3, 802 (2007)   

Local Signatures and Spectral Inversion of Bosonic Mode Coupling in a High-Temperature Superconductor

High-resolution spectroscopy and mapping of the high-temperature superconductor Bi$_{2}$Sr$_{2}$Ca$_{0.93}$Y$_{0.07}$Cu$_{2}$O$_{8+d}$ was performed with a custom-built low-temperature scanning tunneling microscope. At optimal doping ($T_{c} \quad \approx $ 96 K), these materials exhibit~unusually strong spectral sidebands characteristic of electron-boson coupling. The magnitude of these Holstein-like $d$-wave density of states replicas facilitates a spectral inversion procedure, from which the critical parameters of the bosonic coupling can be directly extracted. This results in electron-boson coupling $\lambda \quad \approx $ 0.2-0.4 and boson energy $\Omega \quad \approx $ 70-90 meV.~Origins and implications of these excitations will be discussed.