### Session S9: Optical Properties of Superconductors

 Wednesday, March 12, 2008 2:30PM - 2:42PM S9.00001: Superconducting plasma edge along the \boldmath $c$ axis in La$_{2-x}$Ba$_x$CuO$_4$\unboldmath C. C. Homes , M. H\"{u}cker , Jinsheng Wen , Zhijun Xu , G. D. Gu , J. M. Tranquada The optical properties of La$_{2-x}$Ba$_x$CuO$_4$ (LBCO) have been measured for a number of temperatures over a wide frequency range along the poorly-conducting $c$ axis for the $x=0.095$, $0.125$ and $0.155$ Ba concentrations. In slightly underdoped LBCO ($x=0.095$, $T_c\simeq 32$~K), a sharp plasma edge is observed in the reflectance at low frequency below $T_c$; this plasma edge is associated with Josephson coupling of the copper-oxygen planes and the formation of a bulk three-dimensional superconducting state. A plasma edge is also observed in the more heavily-doped material ($x=0.155$, $T_c\simeq 32$~K) below $T_c$ at higher frequency; however, it is significantly broader in character. Interestingly, for the $x=1/8$ doping, static charge and spin stripe order develop at 54 and 42~K, respectively; the superconducting transition is strongly suppressed ($T_c\simeq 3$~K) and the plasma edge is not observed. The failure to observe a plasma edge for this doping is consistent with the recently proposed view that the layers are decoupled due to the formation of spin stripes, blocking the formation of a coherent three-dimensional superconducting state. Wednesday, March 12, 2008 2:42PM - 2:54PM S9.00002: Investigation of the bosonic spectral density in highly under-doped YBa$_{2}$Cu$_{3}$O$_{6.35 }$ Jing Yang , Thomas Timusk , Douglas Bonn , Ruixing Liang , Walter Hardy We studied the doping dependence of the bosonic spectral function in nearly optimally-doped La$_{2-x}$Sr$_{x}$CuO$_{4}$, ortho-II YBa$_{2}$Cu$_{3}$O$_{6.35 }$and highly under-doped YBa$_{2}$Cu$_{3}$O$_{6.35}$ single crystals by optical spectroscopy. With fixed oxygen content, the hole doping of the YBCO system can be fine-tuned by varying the degree of oxygen ordering. After annealing and quenching, we were able to make oxygen less ordered and obtain a highly under-doped YBa$_{2}$Cu$_{3}$O$_{6.35 }$ sample with a very low transition temperature around 18K (about 20{\%} of the optimal T$_{c})$. The a-axis reflectance data of this sample at nine temperatures between 30K and 295K were measured with an infrared spectrometer between 60 and 40 000 cm$^{-1}$ with the aid of three different infrared and optical polarizers. The optical properties of the highly under-doped YBCO sample show dramatic changes compared to the ortho-II YBCO sample. The strong sharp mode in the bosonic spectral function \textit{$\alpha$}$^{2}$\textit{F($\Omega )$ }in the ortho-II YBCO is absent in the highly under-doped sample. Wednesday, March 12, 2008 2:54PM - 3:06PM S9.00003: Optical conductivity of electron-doped cuprates, pseudogap and antiferromagnetic fluctuations D. Bergeron , B. Kyung , V. Hankevych , A.-M.S. Tremblay Recent neutron scattering experiments on electron-doped cuprates have shown that the antiferromagnetic correlation length at the pseudogap temperature scales like the thermal de Broglie wavelength. This result, predicted by the Two-Particle Self-Consistent approach (TPSC), suggests that antiferromagnetic fluctuations are at the origin of the pseudogap in electron-doped cuprates. Clearly one needs to verify that other physical properties can also be explained within the same formalism. We thus derive, within TPSC, the formula appropriate for optical conductivity, including the first vertex correction. Our numerical calculations then show that, as observed experimentally, there is a transfer of spectral weight from low to high energy when antiferromagnetic correlations become important near the pseudogap temperature. Wednesday, March 12, 2008 3:06PM - 3:18PM S9.00004: Optical Properties of Organic Superconductor $\kappa$-(BETS)$_2$FeBr$_4$ M. Reedyk , N. Hossein Khah , B. Liu , G.V. Sudhakar Rao , H. Fujiwara , H. Kobayashi , M.A. Tanatar , K. Yakushi , T. Nakamura The optical response to far- and mid-infrared radiation has been measured for quasi two-dimensional plate-shaped crystals of $\kappa$-(BETS)$_2$FeBr$_4$ [where BETS = bis(ethylenedithio)-tetraselenafulvalene]. $\kappa$-(BETS)$_2$FeBr$_4$ is the first antiferromagnetic organic superconductor at ambient pressure with N\'{e}el temperature T$_N=2.5$ K and superconducting transition temperature T$_C=1.1$ K. Polarized thermal reflectance measurements were performed to compare the reflectance above and below T$_C$ and T$_N$ using a Martin-Puplett-type polarizing interferometer and $^3$He cryostat. In addition polarized absolute reflectance measurements in the far- and mid-infrared were carried out at temperatures in the normal state between 4 K and 300 K using a Michelson interferometer and cold finger cryostat. Kramers-Kronig analysis was then used to determine the optical conductivity of $\kappa$-(BETS)$_2$FeBr$_4$ at these temperatures. Wednesday, March 12, 2008 3:18PM - 3:30PM S9.00005: Optical properties of lattice/spin polarons in underdoped cuprates Simone Fratini , Sergio Ciuchi , Emmanuele Cappelluti In this contribution we investigate the optical spectra of one hole in the Holstein-$t$-$J$ model. We employ a dynamical mean-field theory which becomes exact in the limit of infinite connectivity. This allow us to investigate the local (incoherent) features which are related to the internal structure of the polaron, disregarding coherent motion which should be reflected in the Drude-like peak. We show that magnetic and electron-phonon interactions sustain each other in establishing polaronic regime. Polaron formation is reflected in a peculiar mid-infrared (MIR) band which is however notably different in the case of a lattice or magnetic origin. The dependence of $\sigma(\omega)$ on the electron-phonon coupling constant $\lambda$, on the exchange interaction $J$ and on temperature $T$ is investigated. We compare our results with experimental data in Nd$_{2-x}$Ce$_x$CuO$_4$ showing that the doping and temperature dependences of the optical conductivity in this compounds is naturally reproduced by a spin/lattice polaronic model. Wednesday, March 12, 2008 3:30PM - 3:42PM S9.00006: Optical Conductivity and Correlation Strength of the High T$_c$ Cuprate Superconductors Massimo Capone , Armin Comanac , Luca de' Medici , Andrew Millis High temperature copper-oxide-based superconductivity is obtained by adding carriers to insulating parent compounds.'' It is widely believed the parent compounds are Mott'' insulators, in which the lack of conduction arises from anomalously strong electron-electron repulsion, and that the unusual properties of Mott insulators are responsible for high temperature superconductivity. This paper presents a comparison of optical conductivity measurements and theoretical calculations based on Dynamical Mean-Field Theory which challenges this belief: the analysis indicates that the correlation strength in the cuprates is not as strong as previously believed, that the materials are not properly regarded as pure Mott insulators, that antiferromagnetism is essential to obtain the insulating state and, by implication, that antiferromagnetism is essential to the properties of the doped metallic and superconducting state as well. Wednesday, March 12, 2008 3:42PM - 3:54PM S9.00007: Is the Optical Sum Rule Violated in Cuprates? Michael Norman , Andrey Chubukov , Erik van Heumen , Alexey Kuzmenko , Dirk van der Marel Much attention has been given to a possible violation of the optical sum rule in the cuprates, and the connection this might have to kinetic energy lowering. The true optical integral is composed of a cut-off independent term (whose temperature dependence is a measure of the sum rule violation), plus a cut-off dependent term that accounts for the extension of the Drude peak beyond the upper bound of the integral. We find that optical data in the normal state of the cuprates can be accounted for solely by the latter term, implying that the dominant contribution to the observed sum rule `violation' in the normal state is due to the finite cut-off. Wednesday, March 12, 2008 3:54PM - 4:06PM S9.00008: Sum rule analysis of YBa$_2$Cu$_3$O$_y$ in magnetic field Andrew LaForge , Willie Padilla , Kenneth Burch , Zhiqiang Li , Alexander Schafgans , Kouji Segawa , Yoichi Ando , Dimitri Basov We present infrared magneto-optical reflectance measurements which characterize the interplane transport of three dopings of YBa$_2$Cu$_3$O$_y$. An optical sum rule analysis reveals the field-evolution of the energy scale from which the superconducting condensate is drawn. We find that fields applied parallel to the $c$ axis totally suppress high-energy contributions to the condensate in underdoped samples while only moderately reducing the superfluid density. For optimally doped crystals the sum rule is satisfied and not modified by field. These results point toward a more conventional, BCS-like condensation mechanism, and will be discussed in relation to the interlayer phase coherence. Wednesday, March 12, 2008 4:06PM - 4:18PM S9.00009: Illustration of advantages of optical self-energy for understanding conductivity data on superconductors E.J. Nicol , J.P. Carbotte Over the last 20 years, it has become common to present optical data on exotic superconductors, such as high $T_c$ and heavy fermions, in terms of a generalized optical self-energy. However, this quantity has never been fully examined in the context of conventional superconductivity and tested against experiment. We present a detailed study of the optical scattering rate and mass renormalization with emphasis upon the role of elastic and inelastic scattering, and make comparison with recent high quality data. This illustrates the usefulness of this approach and the new insights that can be obtained. Wednesday, March 12, 2008 4:18PM - 4:30PM S9.00010: Optical properties of underdoped high $T_c$ superconductors from a phenomenological model E. Illes , E.J. Nicol , J.P. Carbotte We calculate the optical conductivity predicted by a phenomenological model for the pseudogap state given by Yang, Rice and Zhang [1]. In particular, we present results for both pseudogap and superconducting states as a function of doping. In addition to the conductivity, we examine the optical self-energy (i.e. the optical scattering rate and mass renormalization) and discuss our results in light of experiment. \newline [1] K.Y. Yang, T.M. Rice and F.C. Zhang, Phys. Rev. B 73, 17541 (2006). Wednesday, March 12, 2008 4:30PM - 4:42PM S9.00011: Signatures of superconducting gap inhomogeneities in the optical conductivity J. LeBlanc , E.J. Nicol , J.P. Carbotte The observation of energy gap inhomogeneities in the BISSCO high $T_c$ cuprates motivates studying such effects on other properties. We have calculated the optical conductivity using an effective medium approximation to mix superconducting regions with different energy gaps. We present our results and comment on possible signatures in the conductivity and optical self-energy. Wednesday, March 12, 2008 4:42PM - 4:54PM S9.00012: Time resolved Raman scattering on the pair-breaking peak in Bi-2212 -- direct observation of the dynamics of the superconducting order parameter Pelangi Saichu , Ilka Mahns , Arne Goos , Stephan Binder , Stefan Singer , J. Unterhinninghofen , Benjamin Schulz , Andrivo Rusydi , S.L. Cooper , M.V. Klein , P. Guptasarma , Dirk Manske , Michael Ruebhausen We employ a novel time resolved two-color pump probe Raman technique to study the electronic dynamics in the superconducting state of the high temperature superconductor Bi-2212. By studying the temporal evolution of the gap and the pair-breaking peak in the superconducting state, we reveal two contributions to the superconducting order parameter that respond within 1 ps and 7 ps, respectively. Both effects conserve spectral weight in the sense that the suppression of the pair-breaking peak appears concomitantly with the build up of in-gap states. The recovery times for both contributions to the gap are different by a factor of 4 outlining fundamentally different coupling mechanisms. Wednesday, March 12, 2008 4:54PM - 5:06PM S9.00013: Electronic Raman scattering in cuprates William Guyard , Mathieu Le Tacon , Maximilien Cazayous , Alain Sacuto , Antoine Georges , Doroth\'ee Colson , Anne Forget We report electronic Raman response in mercury compound. In cuprates, the superconducting gap reaches its maximum values along the antinodal directions and vanishes along nodal directions corresponding respectively to the principal axes and the diagonal in the Brillouin zone. We will present both the antinodal ($B_{1g}$) and nodal ($B_{2g}$) responses as a function of doping and temperature. We will also report the full symmetric Raman response ($A_{1g}$) as a function of doping. Wednesday, March 12, 2008 5:06PM - 5:18PM S9.00014: Self Energy Corrections to Resonant Inelastic X-ray Scattering in the Cuprates Wael Al-Sawai , Robert Markiewicz , Arun Bansil Resonant inelastic x-ray scattering (RIXS) is emerging as a powerful probe of strongly correlated systems by providing direct momentum-resolved information on charge excitations across the Mott gap. We have shown recently that long-range Coulomb interactions and self-energy corrections play an important role in modifying the electronic spectra of the cuprates.[1,2] Here we discuss model calculations to explore how plasmon and magnon corrections to the self-energy influence the RIXS spectra of the cuprates. \newline\noindent [1] R.S. Markiewicz and A. Bansil, Phys. Rev. B{\bf 75}, 020508 (R) (2007). \newline\noindent [2] R.S. Markiewicz, S. Sahrakorpi, and A. Bansil, cond- mat/0701524, to be published, PRB. Wednesday, March 12, 2008 5:18PM - 5:30PM S9.00015: Optical conductivity in strongly correlated electron materials Jianmin Tao , Jian-Xin Zhu Ultrafast optical phenomena are of fundamental importance in the investigation of electronic structures of strongly correlated electron materials [1]. Starting from the Hamiltonian of a correlated electron material exposed to a time-dependent laser field, we formulate the particle current density. Within a mean-field approximation, we express the current density in terms of the expectation values of quasiparticle density operators by performing the canonical transformation. Within the Heisenberg picture, we solve a set of equations of motion for these quasiparticle densities. Finally we calculate the optical conductivity in several typical systems. [1] R. D. Averitt and A. J. Taylor, J. Phys: Condensed Matter 14, R1357 (2002).