Session A23: Superconductivity: ARPES on BSCCO and SRO

Deviation from d$_{x^2-y^2}$ gap form in Bi2201 revealed by photon-energy-dependent ARPES study

Previous ARPES studies on optimally doped cuprate superconductor Bi2201 with moderate incident photon energies ($>$ 20 eV) reported that the gap function deviates from simple d$_{x^2-y^2}$ functional form in the antinode, implying that the pseudogap is different from superconductivity. On the other hand, some other ARPES studies using low photon energies ($<$ 10 eV) found that simple d$_{x^2-y^2}$ functional form extends to the antinode, suggesting that the pseudogap has the same origin as superconductivity. We study this contradiction by photon-energy-dependent ARPES. We show that, at low photon energies, background signal is dominant in the antinode and conceals the true gap magnitude. This confirms that the gap function in optimally doped Bi2201 is not simple d$_{x^2-y^2}$ functional form, and supports that the pseudogap is different order from simple superconductivity.   

Laser-ARPES studies on Bi-2212

Temperature-dependent ARPES measurements of the gap function in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ (Bi-2212) have given support for a `two-gap' picture, where superconductivity and the pseudogap represent competing states, but the dichotomy between these gaps in momentum space and temperature is subtle. For instance, the pseudogap is observed by spectroscopy even below T$_{c}$, and ARPES observes superconducting quasiparticles in Bi-2212 even in the antinodal region, where the pseudogap is dominant. Thus, the gap measured at a particular momentum may contain contributions from both states. We have performed laser ARPES measurements on underdoped Bi-2212, using the superior energy resolution of this technique in conjunction with a detailed doping-and-temperature-dependence study, to elucidate the relative contributions of the pseudogap and superconducting gap at different temperatures and momenta. We report our findings on how the superconducting gap evolves into the pseudogap for various dopings.   

Structural origin of apparent Fermi surface pockets in angle-resolved photoemission of Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$

We observe {\it apparent} hole pockets in the Fermi surfaces of single-layer Bi-based cuprate superconductors from angle-resolved photoemission (ARPES). However, from an analysis of their polarization-dependence and detailed low-energy electron diffraction measurements, we show that these are not intrinsic, but due to multiple overlapping superstructure replicas of the main and shadow bands. We demonstrate that the hole pockets reported recently from APRES [Meng~{\it et al.}, Nature {\bf 462}, 335 (2009)] have a similar structural origin, and are inconsistent with an intrinsic hole pocket associated with the electronic structure of a doped CuO$_2$ plane. The true nature of the Fermi surface topology in the enigmatic pseudogap phase therefore remains an open question.   

Photoemission Evidence for New Microscopic Scaling Relation in the Cuprate Superconductors

We use angle resolved photoemission spectroscopy (ARPES) to investigate the relationship between the superconducting gap at low temperature and the quasiparticle scattering rates in the normal state, on the Fermi arc, for optimal and underdoped Bi2212 cuprate high temperature superconductors. Combining these results with similar data on Bi2201 from the literature we find evidence of a new and simple microscopic scaling relation connecting the normal and superconducting states of the cuprates. The result suggests that while nodal-region Cooper pairs decohere above T$_{c}$ they retain the signature of a strong pairing amplitude. The anomalous momentum dependence of excitation lifetimes on the Fermi arc, above T$_{c}$, are dominated by the same interactions that induce superconductivity at and below T$_{c}$.   

Evidence for Strong Forward Scattering and Coupling to Acoustic Phonon Modes in the High-Tc Cuprates

The improved resolution of laser ARPES has revealed the presence of a new low-energy kink in the nodal dispersion of Bi$_2$Sr $_2$Ca$_2$Cu$_2$O$_{8+\delta}$, occuring at an energy below the maximum of the superconducting gap. This observation makes it difficult to interpret this renormalization in terms of coupling to any sharp bosonic modes. We examine coupling to the in-plane acoustic phonon branch via the modulation of the screened Coulomb interaction as an alternative explanation. We demonstrate that such a coupling is strongly peaked in the forward scattering direction and the resulting kink occurs at an energy shifted by the local gap $\Delta(\bf{k})$. Considerations for the reduction in screening with underdoping also provides a mechanism for understanding the doping dependence of the kink. These results indicate the importance of coupling to the acoustic branch with a strong forward scattering peak with important implications for the cuprates.   

The single-particle self-energy and fluctuation spectrum of slightly underdoped Bi2212 from ARPES experiment

We extract the single particle self-energy $\Sigma(\theta,\omega) $ and Eliashberg function $\alpha^2 F(\theta,\omega)$ of normal and superconducting state Bi2212 from ARPES experiments. The self-energies along the cuts at tilt angle $\theta$ were extracted by fitting ARPES momentum distribution curves. Then, using the extracted self-energy as input, the Eliashberg function is deduced by inverting the d- wave Eliashberg equation employing the adaptive maximum entropy method (MEM). The momentum dependence of self-energy was decomposed in terms of $\Sigma(\theta,\omega) = \Sigma_{0}(\omega) + \Sigma_{4}(\omega) cos4\theta $ at 16, 70, 80, 97, and 107 K. We will present the temperature evolution and momentum dependence of the deduced Eliashberg function and self-energy.   

Emergence of superconductivity in HighTc copper oxide superconductors via two crossovers

From our detailed ARPES measurements on BISCO 2212 High Tc Superconductors we found that unlike in conventional superconductors, where there is a single temperature scale Tc separating the normal from the superconducting state, HTSCs exhibit with two additional temperature scales. One is T*, below which electronic excitations are gapped. And the other one is Tcoh, below which electronic states are long-lived. We observed that T* and Tcoh change strongly with doping. They cross each other near optimal doping. There is a region in the normal state where the single particle excitations are gapped as well as coherent. Quite remarkably, this is the region from which superconductivity with highest Tc emerges. Our experimental finding that the two crossover lines intersect is not consistent with a ``single quantum critical'' point near optimal doping, rather it is more naturally consistent with theories of superconductivity for doped Mott insulators.   

Low energy kink in the band dispersions of Sr$_{2}$RuO$_{4}$ studied by ARPES

In Sr$_{2}$RuO$_{4}$ , incommensurate antiferromagnetic fluctuations (IAF) were reported to have 4 - 10 meV energy with \textbf{q} = (0.6$\pi $, 0.6$\pi )$ while the lowest optical phonon is at 12meV. If an electron is coupled to AIF in Sr$_{2}$RuO$_{4}$, the electronic band dispersions will kink below 10meV. Then, one can attribute the low energy kinks below 10meV to the electron-IAF coupling. In spite of the fact that multiple kink energies were recently reported in Sr$_{2}$RuO$_{4}$, kinks below 10meV has not been observed. To look for the so far unobserved electron-IAF coupling in Sr$_{2}$RuO$_{4}$, we performed ultra high resolution angle resolved photoemission (ARPES) experiments on Sr$_{2}$RuO$_{4}$ with clean surfaces. In the results, we observe kinks in the band dispersions at energies below 10 meV which show strong momentum dependence. To elucidate the origin of these new kinks, we compare ARPES results with inelastic neutron scattering and band calculation results.   

ARPES lineshapes, coherent to incoherent ratios, and the waterfall self-energy of Bi2212 cuprate superconductors

We report a detailed lineshape analysis of ARPES data on Bi2212 in which we separate out the sharp coherent peaks from the higher energy incoherent ``background'' portions, which includes and makes up the famous waterfall regions. We find that the ratio of the incoherent to coherent weights scales quadratically with the peak energy of the coherent portion of the spectra over a very wide energy range. We show that this behavior, including the waterfalls, can be understood with a simple model electron self-energy, giving a new and powerful experimental tool for determining self-energy effects in correlated electron systems.   

Effects of a particle-hole asymmetric pseudogap on Bogoliubov quasiparticles in ARPES

Motivated by recent angle-resolved photoemission experiments (ARPES) on the underdoped cuprates [1], we show that the particle-hole asymmetry of the pseudogap energy bands acts to reveal new spectral peaks due to Bogoliubov quasiparticles in the superconducting state. With sufficient broadening, the Bogoliubov peaks will merge with existing peaks and will lead to the anomalous observation, seen in experiment, that the carrier spectral density appears to broaden with reduced temperature. Using the resonating valence bond (RVB) spin liquid model [2], we compare with recent experimental data to empirically determine the temperature dependence of the pseudogap. Further, we demonstrate that the d-density wave model cannot explain the same data.\\[4pt] [1] Hashimoto et al. Nature Physics \textbf{6} 414.\\[0pt] [2] K.Y Yang, T.M. Rice and F.-C. Zhang, PRB \textbf{73} 17541 (2006).   

Intrinsic Scattering Rates and the ``Filling'' Gap of Bi2212

As a direct measure of the electronic interactions in a solid, knowledge of the electronic scattering rates is essential for understanding a material's behavior. Since angle resolved photoemission spectroscopy (ARPES) can probe an individual momentum state, it holds great promise for the most detailed and accurate measurements of the k-dependent electron scattering rates. Unfortunately, the scattering rates determined from ARPES are typically an order of magnitude greater than those obtained from other probes, (e.g. optical spectroscopy). Here we present a new type of spectrum, the ARPES tunneling spectrum (ATS), which resolves this discrepancy, as well as provides a qualitatively different understanding of the gaps and scattering rates along the Fermi surface. Applying this technique to the study of Bi2212, we find that the scattering rates are approximately independent of Fermi surface position but grow exponentially with temperature. Furthermore, we find that this strongly temperature dependent scattering rate is the source of the long observed but not understood ``filling'' of the superconducting gap in the cuprates.   

Pairing fluctuations determine low energy electronic spectra in cuprate superconductors

Over the years, Angle Resolved Photo Emission Spectroscopy (ARPES) has uncovered a number of unusual spectral properties of near Fermi energy electrons with definite in-plane momenta in the hole doped cuprates. We describe here a minimal theory of tight binding electrons moving on the square planar Cu lattice of the cuprates, mixed quantum mechanically with pairs of them (Cooper pairs); superconductivity occurring at $T_c$ is their long range ($d$-wave symmetry) phase coherence. Fluctuations necessarily associated with incipient long range superconducting order have a generic large distance behavior near $T_c$. We calculate the spectral density of electrons coupled to such Cooper pair fluctuations and show that properties observed in ARPES above $T_c$ for different cuprates as a function of doping $x$ and temperature $T$ emerge inevitably; e.g. the `Fermi arcs' with $T$ dependent length and an antinodal pseudogap which fills up linearly as $T$ increases towards the pseudogap temperature $T^*$. Below $T_c$, the effects of nonzero superfluid density and thermal fluctuations are calculated and compared successfully with experiment.   

The0ry 0f Dipolon-Phonom Interaction and Isotope Shift in Superconducting Cuprates

Quite recently we have deduced five principles of photoemission and not only we have explained the observed low energy kink but we have also predicted two more high energy kinks [1,2] in quasiparticle energydistribution which have now been observed experimentally, all by means of the dipolon theory [3,4]. Here, the Hamiltonian for the interaction of dipolons with phonons will be presented.The Hamiltonian requires the evaluation of phonon-generated dynamic polarization fields at the oxygen sites in the $Cu-O_2$-planes. The quasi-dipolons (phonon-dressed dipolons) now play role as mediators of electron-electron pairing. Expression for the change in the transition temprature $T_C$ due to change in oxygen isotopic mass has been derived. We have found a small decrease of about 1 per cent in $T_C$ due to $^{16}O\rightarrow^{18}O$ , in agree ment with experiments [5]. The change in dipolon frequencies owing to the interaction with phonons has been calculated. [1] R. R. Sharma, ``Dipolon Theory of Kink Structure.....'', in Superconducting Cuprates....", Ed. K. N. Courtlandt, P. 81-100, Nova Sc, Pub., New York, 2009. [2] R. R. Sharma, Physica {\bf C 468}, 190 (2008). [3] R. R. Sharma, Phy. Rev. {\bf B 63}, 054506 (2001). [4] R. R. Sharma, Physica {\bf C 439}, 47 (2006). [5] J. p. Franck in Physical Properties.....IV, Ed. D. M. Ginsberg, P. 189-293,World Scientific, Singopore, 1994.   

New Fermi Surface Sheets Revealed in Sr2RuO4 Revealed by High Resolution Angle-Resolved Photoemission Spectroscopy

We will present our detailed Fermi surface measurements on Sr2RuO4 by high resolution angle-resolved photoemission spectroscopy (ARPES) including vacuum ultra-violet (VUV) laser-based ARPES. In addition to the three sets of Fermi surface sheets originating from the bulk bands, the surface bands and the shadow bands of the surface bands, we have revealed two new Fermi surface sheets. The origin of these new Fermi surface sheets will be discussed.   

Anisotropic mass renormalization in Sr2RuO4

The layered perovskite Sr$_{2}$RuO$_{4}$ continues to attract interest as a model system of a multiband Fermi liquid. Previous dHvA and ARPES studies successfully determined its Fermi surface [1, 2] and reported a large and sheet dependent renormalization of the Fermi velocity due to electron-electron interactions with v$_{band}$/v$_{F}$ ranging from $\approx$ 3 for the d$_{xz/yz}$ derived $\alpha$ and $\beta$ sheets to $\approx$ 5.5 for the $\gamma$ sheet with dominant dxy orbital character [1, 3]. Here, we report new high-resolution ARPES data revealing an additional strong momentum dependence of the renormalization within a single Fermi surface sheet. This effect is most pronounced in the $\gamma$ band and is larger than expected from the mixing of the orbital composition along individual Fermi surface sheets induced by spin-orbit coupling [4,5]. Our observations therefore provide evidence for a genuinely momentum dependent self-energy in the vicinity of a van Hove singularity. \\[0pt] [1] C. Bergemann et al., Advances in Physics 52, 639 (2003) \\[0pt] [2] A. Damascelli et al., Physical Review Letters 85, 5194 (2000). \\[0pt] [3] K.M. Shen et al., Physical Review Letters 99, 187001 (2007). \\[0pt] [4] M.W. Haverkort et al., Phys Rev Lett. 101, 026406 (2008) \\[0pt] [5] J. Mravlje et al., arXiv:1010.5910v1(2010)