Session V34: Superconductivity: Spectroscopy

Comparing the three characteristic electronic excitations in the pseudogap state of underdoped Bi$_{2}$Sr$_{2}$Ca$_{0.8}$Dy$_{0.2}$Cu$_{2}$O$_{8+\delta }$

We investigate the quasiparticle interference processes as a function of temperature for heavily underdoped Bi$_{2}$Sr$_{2}$Ca$_{0.8}$Dy$_{0.2}$Cu$_{2}$O$_{8 }$ (T$_{c}$=42K). We demonstrate that three types of electronic excitations exist in the pseudogap phase: (1) metallic excitations on the Fermi Arc, (2) the Bogoliubov quasiparticle excitations of what appears to be a phase incoherent d-wave superconductor in the confined area in momentum space (Jhinhwan Lee \textit{et al} (2009)) and (3) the high energy pseudogap excitations seen in the anti-nodal region outside the $\surd $2X$\surd $2 Brillouin zone (Y. Kohsaka \textit{et al}. Nature 454, 1072 (2008 ). We discuss the relationship of these three components of the electronic structure to the thermodynamic and transport characterization of this phase.   

Quasiparticle interference above and below $T_c$ in underdoped cuprates

There is considerable debate over the evolution of quasi-particle excitations between the superconducting and pseudogap phases in the underdoped cuprates. In the superconducting phase, dispersive real space modulations are observed [1], which can be explained by quasi-particle interference (QPI), whose location in momentum space is consistent with ARPES. What should happen to these modulations in the pseudogap state, where ARPES indicates a finite arc of gapless Fermi surface? We will present STM data from underdoped $\textrm{Bi}_2\textrm{Sr}_2\textrm{CaCu}_2\textrm{O}_{8+x}$ that investigates the nature of this change and its connection with the non-dispersive features seen above $T_c$ [2]. [1] Kohsaka $\textit{et al. Nature } \textbf{454}$, 1072 (2008). [2] Vershinin $\textit{et al. Science } \textbf{305}$, 1993 (2004).   

Extinction of quasiparticle interference in underdoped cuprates with coexisting order

Recent scanning tunnelling spectroscopy measurements [Y. Koksaka et al., Nature 454, 1072 (2008)] have shown that dispersing quasiparticle interference peaks in Fourier transformed conductance maps disappear as the bias voltage exceeds a certain threshold corresponding to the coincidence of the contour of constant quasiparticle energy with the antiferromagnetic zone boundary. Here we argue that this is caused by quasistatic short-range coexisting order present in the d-wave superconducting phase, and that the most likely origin of this order is disorder-induced incommensurate antiferromagnetism. We show explicitly how the peaks are extinguished in the related situation with coexisting long-range antiferromagnetic order, and discuss the connection with the realistic disordered case. Since it is the localized quasiparticle interference peaks rather than the underlying antinodal states themselves which are destroyed at a critical bias, our proposal resolves a conflict between scanning tunneling spectroscopy and photoemission regarding the nature of these states.   

Quasi-particle interference and vortex ``checkerboard'' in Bi$_2$Sr$_2$CaCu$_2$O$_y$

Relationship between the ``checkerboard'' electronic-state modulation in a vortex core~[1] and the quasi-particle interference effect has been studied using STM/STS in optimally- doped Bi$_2$Sr$_2$CaCu$_2$O$_y$. We found that the vortex- induced signals in Fourier-transform spectroscopic images appear in the close vicinity to some of the ``octet'' scattering vectors for the quasi-particle interference~[2], suggesting that the vortex ``checkerboard'' is associated with the Fermi momentum. Conductance spectrum taken at the center of the vortex core shows a sharp peak at a low energy ($\sim$ meV) in the empty state. We argue the possible relationship between these observations and the quantum-limit nature of the vortex core. [1] J. E. Hoffman {\it et al.}, Science {\bf 295}, 466 (2002). [2] K. McElroy {\it et al.}, Nature {\bf 422}, 592 (2003).   

Quasiparticle scattering from impurities in the cuprates

Scanning tunneling spectroscopy (STS) measurements have shown that the local density of states in the cuprate superconductors is spatially inhomogeneous. Fourier-transformed STS has been used to investigate the mixing of momentum space eigenstates of the superconducting quasiparticles in the presence of this inhomogeneity, and has observed the extinction of the quasiparticle peaks upon approaching the antinodal region of the Fermi surface. We present calculations of momentum dependent quasiparticle scattering from impurity sites. Our results demonstrate that the quasiparticle extinction observed in FT-STS can be interpreted as resulting from the momentum dependence of the quasiparticle scattering rather than the absence of the quasiparticle itself. This interpretation agrees with recent ARPES measurements that observe quasiparticle peaks over the entire Fermi surface.   

Echolocation of Scatterers by Quasiparticles in Cuprate Superconductors

How much can STM techniques tell us about the realization of disorder in a particular sample under study? We propose a new method of STM-data analysis which allows for the determination of the position and strength of impurities/scatterers. Furthermore, for cuprates, it can potentially be used to distinguish if the scatterer is ``ordinary'' or ``anomalous"~\footnote{T. S. Nunner et al, Phys. Rev. B, \textbf{73}, 104511 (2006)}, i.e. part of the pairing potential. The method relies on quasiparticle interference \footnote{Q. Wang and D.-H.~Lee, Phys. Rev. B \textbf{67}, 020511 (2003)} as observed in cuprates$^3$. As for much of the STM phenomenology in cuprates$^{1-3}$, our starting point is the existence of well-defined Bogoliubov quasiparticles defined by a quadratic phenomenological Hamiltonian with intrinsic disorder. By \emph{Energy} ``Fourier-Transform''ing the measured local density of states (LDOS) spectrum from a single point, one can extract the ``echo'' time that a quasiparticle takes to go to and return from a nearby scatterer; doing this at several points in a local patch allows a ``sonar''-like echolocation of the scatterer. This method is complementary to Fourier-Transform Scanning Tunneling Spectroscopy \footnote{K. McElroy et al, Nature, \textbf{422}, 592 (2003)} wherein \emph{Space} Fourier transforms of LDOS data yield the quasiparticle dispersion.   

Interference of nematic quantum critical quasiparticles: a route to the octet model

Given the presence of glassiness and inhomogenaity in cuprate superconductors, the capability of quasiparticle interference (QPI) in inferring momentum space electronic structure from real space local density of states(LDOS) images is surprising. Particularly, the simplicity of the QPI image, a set of well defined dispersing peaks is striking. Regarding the nature of QPI peaks, the ``octet model'' was based on the observation that the peak positions are determined by the eight tips of the ``banana'' shaped qp equal energy contours. However, a key open question has the mechanism for the accumulation of coherence at the tips. Here we show that nematic quantum critical fluctuations, combined with the known extreme velocity anisotropy, provide a natural mechanism for the accumulation of coherence at those special points [1]. Our results raise the intriguing question of whether the nematic fluctuations provide the unique mechanism for such a phenomenon.\\[4pt] [1] E.-A. Kim and M. J. Lawler, arXiv:0811.2242.   

Tunneling-mediated Impurity Resonances in Bilayer Cuprate Superconductors

We have studied tunneling-mediated local density of states (LDOS) of the surface layer of a bilayer cuprate, where a Zn impurity is located on the second Cu-O layer. When the tunneling strength between two Cu-O layers is larger than a critical value, the LDOS on the site just above the Zn impurity first exhibits a resonant peak near the Fermi surface. The larger the tunneling strength, the stronger the resonant peak. It is also shown that the height of the resonant peak oscillates decreasingly with the distance from the site just above the Zn impurity. The location of the resonant peak in the surface LDOS depends on doping, energy gap, and the tunneling strength, and has an opposite bias voltage to that on its nearest neighboring sites. The results could be tested by the STM experiments and be used to further understand the electronic properties of high temperature superconductors.   

Spin Filtering and Dephasing through an Aluminum Nanoparticle

Measurements of spin-polarized current through a single Al nanoparticle in weak tunnel contact with two ferromagnets will be discussed. As a function of the bias voltage across the particle, spin polarized current saturates within the first few discrete energy levels above the ground state. The saturation is related to the energy dependence of the spin relaxation time T$_{1}$, from which we find that T$_{1}$ is about microsecond for the lowest excited state. Spin polarized current is extremely sensitive with respect to the direction of the applied magnetic field relative to magnetization. The discrete levels filter the spin of transmitted electrons along the direction specified by the applied magnetic field, explaining the directional dependence both qualitatively and quantitatively. In zero magnetic field, the filtering direction is determined by the field of the environment, making spin-filtering a new technique to study electron spin-dephasing in single metallic particles and other quantum dots. The spin-dephasing time in the nanoparticle at 4.2K is T$_{2 }>$8ns.   

Possible competing order-induced Fermi arcs and self-consistent gap evolution with temperature in cuprate superconductors

We explore, via numerical simulations, the possibility that competing orders (CO's) induce both the pseudogap (PG) and Fermi arc phenomena in cuprate superconductors. We find that both phenomena occur in hole-type cuprates if (1) a CO arises below a PG temperature T*, which is greater than the superconducting transition temperature, T$_{C}$, and (2) the periodic wave-vector of the CO, \textbf{Q}, is parallel to the Cu-O bonding direction. In contrast, neither phenomena is observed in electron-type cuprates because T*$<$T$_{C}$, but we find evidence that the CO scenario may explain the so-called non-monotonic d-wave gap observed in electron-type cuprates for T$<$T$_{C}$ if \textbf{Q }is parallel to the nodal direction, as in the case of commensurate spin density waves. Finally, we consider a candidate model for self-consistently calculating the superconducting and CO energy gaps as a function of temperature and doping in the hole-type cuprates, as well as estimating the value of T*. Ref.: B.-L. Yu, \textit{et.al. }[arxiv:0804.4028].   

How does the gap change at $T_c$ in underdoped cuprates?

Many measurements on underdoped cuprates have shown a gap that persists up to room temperature. This raises an important question: what happens at $T_c$ in order to cause the loss of perfect conductivity? In ARPES, the nature of the gap changes from d-wave below $T_c$ to Fermi arcs above $T_c$. However, ARPES necessarily averages over significant nanoscale disorder. We will present detailed STM spectroscopy on underdoped $\textrm{Bi}_2\textrm{Sr}_2\textrm{CaCu}_2\textrm{O}_{8+x}$ from both single points and areal averages. By using a local probe we avoid averaging over the disorder. We have performed lattice tracking spectroscopy on identical atomic sites [1] and indentical grids of points [2] for a range of temperatures both below and above $T_c$. Unlike overdoped samples, the STM spectrum in underdoped cuprates shows two energy scales [1]. We will compare our data to models based on ARPES, with emphasis on the difference between the superconducting and pseudogap phases. [1] Gomes \textit{et al., Nature} \textbf{447}, 569 (2007) [2] Pasupathy \textit{et al., Science} \textbf{320}, 196 (2008)   

The Effect Of Spontaneous Magnetization On The Reliability Of The Value For The Spin Polarization As Fitted From Ferromagnet/Superconductor Point Contact Data

The generalized BTK model for charge transport in a ferromagnet/superconductor point contact can be used to estimate the spin polarization in a ferromagnet. However, even when these measurements are carried out in zero applied magnetic field, there can be a substantial field in the active region of the contact due to the spontaneous magnetization of the ferromagnet itself. We estimate the effect of spontaneous magnetization on the reliability of the values of the spin polarization parameter for various ranges in contact transparency, inelastic scattering and temperature.   

Coherence factor effects in the antisymmetrized LDOS correlators

Recent scanning tunneling experiments on underdoped cuprates by Hanaguri et al [1] show the appearance of coherence factor effects. Unlike conventional observables, we show that the tunneling density of states in a superconductor does not have a well defined coherence factor. However, by extracting the component that is either even, or odd in the bias voltage, we show that these separate components have well-defined coherence factors. These results are used to understand the appearance of coherence factor effects in the antisymmetrized local density of states correlators in recent scanning tunneling experiments. \\[3pt] [1] T. Hanaguri, Y. Kohsaka, M. Ono, M. Maltseva, P. Coleman, I. Yamada, M. Azuma, M. Takano, K. Ohishi and H. Takagi, to be published (2009).   

Visualizing electronic segregation in lightly-doped Ca$_{2-x}$Na$_x$CuO$_2$Cl$_2$

We report spectroscopic imaging on evolution of the electronic state in a lightly-doped cuprate superconductor Ca$_{2-x}$Na$_x$CuO$_2$Cl$_2$ across the metal-insulator critical doping. We find nm-scale electronic segregation between regions breaking and showing the lattice symmetry. The former shows C$_2$ symmetry characterized by the unidirectional nano-domains and the V-shaped pseudogap found in superconducting samples [1] while the latter shows C$_4$ symmetry and wider U-shaped gap prominent in non-superconducting samples. This indicates that the local symmetry breaking is inherent in the electronic states created inside the Mott gap by hole doping. We also discuss spectra in C$_2$/C$_4$ domains and superconducting/insulating samples. \par ~ \par \noindent [1] Y. Kohsaka et al., Science 315, 1380 (2007), Nature 454, 1072 (2008).   

Search for Orbital-Current Effects in Y$_{2}$Ba$_{4}$Cu$_{7}$O$_{15-\delta}$ using $^{89}$Y NMR

Recent efforts at explaining the exotic electronic properties of cuprates by involving orbital currents attracted a lot of attention. Here we present $^{89}$Y NMR measurements on an oriented $\mathrm{Y_{2}Ba_{4}Cu_{7}O_{15-\delta}}$ powder sample to search for the possible orbital-current phase. The temperature behavior of the $^{89}$Y line width and the spin-lattice relaxation rate in the normal-conducting phase were investigated in the normal-conducting state of the compound. The study provides upper limits for a static magnetic field and the amplitude of a fluctuating magnetic field at the Y site of $\alt 0.15mT$ and $\alt 0.7mT$, respectively. These values provide significant constraints on possible static or quasi-static orbital currents.