Temperature-Dependent Ellipsometry Measurements of Partial Coulomb Energy in Superconducting Cuprates

Levallois, J.; Tran, M. K.; Pouliot, D.; Presura, C. N.; Greene, L. H.; Eckstein, J. N.; Uccelli, J.; Giannini, E.; Gu, G. D.; Leggett, A. J.; van der Marel, D.

doi:10.1103/PhysRevX.6.031027

Title: Temperature-Dependent Ellipsometry Measurements of Partial Coulomb Energy in Superconducting Cuprates

Journal Article · Wed Aug 24 00:00:00 EDT 2016 · Physical Review. X

DOI:https://doi.org/10.1103/PhysRevX.6.031027· OSTI ID:1305439

Levallois, J.; Tran, M. K.; Pouliot, D.; Presura, C. N.; Greene, L. H.; Eckstein, J. N.; Uccelli, J.; Giannini, E.; Gu, G. D.; Leggett, A. J.; van der Marel, D.

Here we performed an experimental study of the temperature and doping dependence of the energy-loss function of the bilayer and trilayer bismuth cuprates family. The primary aim is to obtain information on the energy stored in the Coulomb interaction between the conduction electrons, on the temperature dependence thereof, and on the change of Coulomb interaction when Cooper pairs are formed. We performed temperature-dependent ellipsometry measurements on several Bi₂Sr₂CaCu₂O_8₋x single crystals: underdoped with T_c=60, 70, and 83 K; optimally doped with T_c=91 K; overdoped with T_c=84, 81, 70, and 58 K; as well as optimally doped Bi₂Sr₂Ca₂Cu₃O_10+xwith T_c=110 K. Our first observation is that, as the temperature drops through T_c, the loss function in the range up to 2 eV displays a change of temperature dependence as compared to the temperature dependence in the normal state. This effect at—or close to—T_c depends strongly on doping, with a sign change for weak overdoping. The size of the observed change in Coulomb energy, using an extrapolation with reasonable assumptions about its q dependence, is about the same size as the condensation energy that has been measured in these compounds. Our results therefore lend support to the notion that the Coulomb energy is an important factor for stabilizing the superconducting phase. Lastly, because of the restriction to small momentum, our observations do not exclude a possible significant contribution to the condensation energy of the Coulomb energy associated with the region of q around (π,π).

View Journal Article

Cite

Export

Save

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States); Energy Frontier Research Centers (EFRC) (United States). Center for Emergent Superconductivity (CES)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Swiss National Science Foundation (SNSF)

Grant/Contract Number:: SC00112704; AC02-07CH11358; SC0012704; AC02-98CH10886

OSTI ID:: 1305439

Alternate ID(s):: OSTI ID: 1336224

Report Number(s):: BNL-113255-2016-JA; PRXHAE; 031027

Journal Information:: Physical Review. X, Journal Name: Physical Review. X Vol. 6 Journal Issue: 3; ISSN 2160-3308

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 23 works

Citation information provided by
Web of Science

References (70)

Cuprate Superconductivity: Dependence of $T_{c}$ on the $c$ -Axis Layering Structure Leggett, A. J. Physical Review Letters, Vol. 83, Issue 2 https://doi.org/10.1103/PhysRevLett.83.392	journal	July 1999
Quantitative test of a microscopic mechanism of high-temperature superconductivity Demler, Eugene; Zhang, Shou-Cheng Nature, Vol. 396, Issue 6713 https://doi.org/10.1038/25482	journal	December 1998
Persistence of the Superconducting Condensate Far above the Critical Temperature of ${YBa}_{2} (Cu, Zn)_{3} O_{y}$ Revealed by $c$ -Axis Optical Conductivity Measurements for Several Zn Concentrations and Carrier Doping Levels Uykur, Ece; Tanaka, Kiyohisa; Masui, Takahiko Physical Review Letters, Vol. 112, Issue 12 https://doi.org/10.1103/PhysRevLett.112.127003	journal	March 2014
The electronic specific heat of cuprate superconductors Loram, J. W.; Mirza, K. A.; Wade, J. M. Physica C: Superconductivity, Vol. 235-240 https://doi.org/10.1016/0921-4534(94)91331-5	journal	December 1994
In-plane optical spectral weight transfer in optimally doped ${Bi}_{2} {Sr}_{2} {Ca}_{2} {Cu}_{3} O_{10}$ Carbone, F.; Kuzmenko, A. B.; Molegraaf, H. J. A. Physical Review B, Vol. 74, Issue 2 https://doi.org/10.1103/PhysRevB.74.024502	journal	July 2006
Generic superconducting phase behavior in high- $T_{c}$ cuprates: $T_{c}$ variation with hole concentration in ${YBa}_{2}$ ${Cu}_{3}$ $O_{7 - δ}$ Tallon, J. L.; Bernhard, C.; Shaked, H. Physical Review B, Vol. 51, Issue 18 https://doi.org/10.1103/PhysRevB.51.12911	journal	May 1995
Point nodes persisting far beyond Tc in Bi2212 Kondo, Takeshi; Malaeb, W.; Ishida, Y. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms8699	journal	July 2015
Correlation effects on the oscillator strength of optical absorption: Sum rule for the one-dimensional Hubbard model Baeriswyl, D.; Carmelo, J.; Luther, A. Physical Review B, Vol. 33, Issue 10 https://doi.org/10.1103/PhysRevB.33.7247	journal	May 1986
The condensation energy and pseudogap energy scale of Bi:2212 from the electronic specific heat Loram, J. W.; Luo, J. L.; Cooper, J. R. Physica C: Superconductivity, Vol. 341-348 https://doi.org/10.1016/S0921-4534(00)00706-1	journal	November 2000
Competing charge, spin, and superconducting orders in underdoped ${YBa}_{2} {Cu}_{3} O_{y}$ Hücker, M.; Christensen, N. B.; Holmes, A. T. Physical Review B, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRevB.90.054514	journal	August 2014
Optical and dc conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point including vertex corrections Bergeron, Dominic; Hankevych, Vasyl; Kyung, Bumsoo Physical Review B, Vol. 84, Issue 8 https://doi.org/10.1103/PhysRevB.84.085128	journal	August 2011
Resonant x-ray scattering study of charge-density wave correlations in ${YBa}_{2} {Cu}_{3} O_{6 + x}$ Blanco-Canosa, S.; Frano, A.; Schierle, E. Physical Review B, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRevB.90.054513	journal	August 2014
Field-Enhanced Diamagnetism in the Pseudogap State of the Cuprate ${Bi}_{2} {Sr}_{2} Ca {Cu}_{2} O_{8 + δ}$ Superconductor in an Intense Magnetic Field Wang, Yayu; Li, Lu; Naughton, M. J. Physical Review Letters, Vol. 95, Issue 24 https://doi.org/10.1103/PhysRevLett.95.247002	journal	December 2005
Quantum cluster theories Maier, Thomas; Jarrell, Mark; Pruschke, Thomas Reviews of Modern Physics, Vol. 77, Issue 3 https://doi.org/10.1103/RevModPhys.77.1027	journal	October 2005
Emergence of charge order from the vortex state of a high-temperature superconductor Wu, Tao; Mayaffre, Hadrien; Krämer, Steffen Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms3113	journal	July 2013
Growth and characterization of Bi ₂ Sr ₂ Ca ₂ Cu ₃ O ₁₀ and (Bi,Pb) ₂ Sr ₂ Ca ₂ Cu ₃ O ₁₀ single crystals Giannini, E.; Garnier, V.; Gladyshevskii, R. Superconductor Science and Technology, Vol. 17, Issue 1 https://doi.org/10.1088/0953-2048/17/1/037	journal	December 2003
Disentangling Cooper-pair formation above the transition temperature from the pseudogap state in the cuprates Kondo, Takeshi; Hamaya, Yoichiro; Palczewski, Ari D. Nature Physics, Vol. 7, Issue 1 https://doi.org/10.1038/nphys1851	journal	December 2010
A "midinfrared" scenario for cuprate superconductivity Leggett, A. J. Proceedings of the National Academy of Sciences, Vol. 96, Issue 15 https://doi.org/10.1073/pnas.96.15.8365	journal	July 1999
Fluctuating stripes at the onset of the pseudogap in the high-Tc superconductor Bi2Sr2CaCu2O8+x Parker, Colin V.; Aynajian, Pegor; da Silva Neto, Eduardo H. Nature, Vol. 468, Issue 7324 https://doi.org/10.1038/nature09597	journal	December 2010
Optical evidence for strong anisotropy in the normal and superconducting states in ${Bi}_{2}$ ${Sr}_{2}$ ${CaCu}_{2}$ $O_{8 + z}$ Tajima, S.; Gu, G. D.; Miyamoto, S. Physical Review B, Vol. 48, Issue 21 https://doi.org/10.1103/PhysRevB.48.16164	journal	December 1993
Electron Interaction in Solids. Characteristic Energy Loss Spectrum Nozières, P.; Pines, D. Physical Review, Vol. 113, Issue 5 https://doi.org/10.1103/PhysRev.113.1254	journal	March 1959
Collective modes of spin, density, phase, and amplitude in exotic superconductors van der Marel, D. Physical Review B, Vol. 51, Issue 2 https://doi.org/10.1103/PhysRevB.51.1147	journal	January 1995
Polarized infrared reflectivity study of an oriented ceramic of Bi 2 Sr 2 Ca 2 Cu 3 O 10 + δ (Bi-2223) Petit, N.; Garnier, V.; Ta Phuoc, V. The European Physical Journal B, Vol. 25, Issue 4 https://doi.org/10.1140/epjb/e20020048	journal	February 2002
Apparent violation of the conductivity sum rule in certain superconductors Hirsch, J. E. Physica C: Superconductivity, Vol. 199, Issue 3-4 https://doi.org/10.1016/0921-4534(92)90415-9	journal	September 1992
NMR study of carrier distribution and superconductivity in multilayered high-Tc cuprates Kotegawa, H.; Tokunaga, Y.; Ishida, K. Journal of Physics and Chemistry of Solids, Vol. 62, Issue 1-2 https://doi.org/10.1016/S0022-3697(00)00122-0	journal	January 2001
Optical spectrum of a Hubbard chain Maldague, Pierre F. Physical Review B, Vol. 16, Issue 6 https://doi.org/10.1103/PhysRevB.16.2437	journal	September 1977
Enhanced Superconducting Gaps in the Trilayer High-Temperature ${Bi}_{2} {Sr}_{2} {Ca}_{2} {Cu}_{3} O_{10 + δ}$ Cuprate Superconductor Ideta, S.; Takashima, K.; Hashimoto, M. Physical Review Letters, Vol. 104, Issue 22 https://doi.org/10.1103/PhysRevLett.104.227001	journal	June 2010
Optical integral in the cuprates and the question of sum-rule violation Norman, M. R.; Chubukov, A. V.; van Heumen, E. Physical Review B, Vol. 76, Issue 22 https://doi.org/10.1103/PhysRevB.76.220509	journal	December 2007
Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy Wu, Tao; Mayaffre, Hadrien; Krämer, Steffen Nature, Vol. 477, Issue 7363 https://doi.org/10.1038/nature10345	journal	September 2011
Difference between Normal and Superconducting States of a Metal Chester, G. V. Physical Review, Vol. 103, Issue 6 https://doi.org/10.1103/PhysRev.103.1693	journal	September 1956
Anomalies in the infrared spectra of underdoped ${Bi}_{2} {Sr}_{2} Ca {Cu}_{2} O_{z}$ as evidence for the intrabilayer Josephson effect Železný, V.; Tajima, S.; Munzar, D. Physical Review B, Vol. 63, Issue 6 https://doi.org/10.1103/PhysRevB.63.060502	journal	January 2001
An organizing principle for two-dimensional strongly correlated superconductivity Fratino, L.; Sémon, P.; Sordi, G. Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep22715	journal	March 2016
Insulator, metal, or superconductor: The criteria Scalapino, Douglas J.; White, Steven R.; Zhang, Shoucheng Physical Review B, Vol. 47, Issue 13 https://doi.org/10.1103/PhysRevB.47.7995	journal	April 1993
Condensation energy and high- $T_{c}$ superconductivity van der Marel, D.; Leggett, A. J.; Loram, J. W. Physical Review B, Vol. 66, Issue 14 https://doi.org/10.1103/PhysRevB.66.140501	journal	October 2002
Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states Lawler, M. J.; Fujita, K.; Lee, Jhinhwan Nature, Vol. 466, Issue 7304 https://doi.org/10.1038/nature09169	journal	July 2010
Electron energy-loss studies of high- T _c superconductors YBa ₂ Cu ₃ O _{7- x} and Bi ₂ Sr ₂ CaCu ₂ O ₈ Nakai, S.; Nücker, N.; Romberg, H. Physica Scripta, Vol. 41, Issue 4 https://doi.org/10.1088/0031-8949/41/4/049	journal	April 1990
Fluctuations and critical temperature reduction in cuprate superconductors Tallon, J. L.; Storey, J. G.; Loram, J. W. Physical Review B, Vol. 83, Issue 9 https://doi.org/10.1103/PhysRevB.83.092502	journal	March 2011
Kinetic energy change with doping upon superfluid condensation in high-temperature superconductors Deutscher, Guy; Santander-Syro, Andrés Felipe; Bontemps, Nicole Physical Review B, Vol. 72, Issue 9 https://doi.org/10.1103/PhysRevB.72.092504	journal	September 2005
Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8+δ Gomes, Kenjiro K.; Pasupathy, Abhay N.; Pushp, Aakash Nature, Vol. 447, Issue 7144 https://doi.org/10.1038/nature05881	journal	May 2007
The doping dependence of T* – what is the real high-Tc phase diagram? Tallon, J. L.; Loram, J. W. Physica C: Superconductivity, Vol. 349, Issue 1-2 https://doi.org/10.1016/S0921-4534(00)01524-0	journal	January 2001
Collective modes of the extended Hubbard model with negative U and arbitrary electron density Kostyrko, T.; Micnas, R. Physical Review B, Vol. 46, Issue 17 https://doi.org/10.1103/PhysRevB.46.11025	journal	November 1992
Kinetic Energy Driven Pairing in Cuprate Superconductors Maier, Th. A.; Jarrell, M.; Macridin, A. Physical Review Letters, Vol. 92, Issue 2 https://doi.org/10.1103/PhysRevLett.92.027005	journal	January 2004
Evidence for Intra-Unit-Cell magnetic order in the pseudo-gap state of high-T _c cuprates Sidis, Y.; Bourges, P. Journal of Physics: Conference Series, Vol. 449 https://doi.org/10.1088/1742-6596/449/1/012012	journal	July 2013
Transverse optical plasmons in layered superconductors van der Marel, D.; Tsvetkov, A. Czechoslovak Journal of Physics, Vol. 46, Issue S6 https://doi.org/10.1007/BF02548125	journal	June 1996
The plasmon density of states of a layered electron gas Morawitz, H.; Bozovic, I.; Kresin, V. Z. Zeitschrift für Physik B Condensed Matter, Vol. 90, Issue 3 https://doi.org/10.1007/BF01433048	journal	September 1993
Interlayer Tunneling Models of Cuprate Superconductivity: Implications of a Recent Experiment Leggett, A. J. Science, Vol. 274, Issue 5287 https://doi.org/10.1126/science.274.5287.587	journal	October 1996
Global and local measures of the intrinsic Josephson coupling in Tl2Ba2CuO6 as a test of the interlayer tunnelling model Tsvetkov, A. A.; van der Marel, D.; Moler, K. A. Nature, Vol. 395, Issue 6700 https://doi.org/10.1038/26439	journal	September 1998
Random-Phase Approximation in the Theory of Superconductivity Anderson, P. W. Physical Review, Vol. 112, Issue 6 https://doi.org/10.1103/PhysRev.112.1900	journal	December 1958
Electronic specific heat of ${YBa}_{2}$ ${Cu}_{3}$ $O_{6 + x}$ from 1.8 to 300 K Loram, J. W.; Mirza, K. A.; Cooper, J. R. Physical Review Letters, Vol. 71, Issue 11 https://doi.org/10.1103/PhysRevLett.71.1740	journal	September 1993
Superconductivity-Induced Transfer of In-Plane Spectral Weight in Bi2Sr2CaCu2O8+delta Molegraaf, H. J. A. Science, Vol. 295, Issue 5563 https://doi.org/10.1126/science.1069947	journal	March 2002
Electrodynamics of a layered electron gas. II. Periodic array Fetter, Alexander L. Annals of Physics, Vol. 88, Issue 1 https://doi.org/10.1016/0003-4916(74)90397-2	journal	November 1974
Approximate solution of ellipsometric equations for optically biaxial crystals Aspnes, D. E. Journal of the Optical Society of America, Vol. 70, Issue 10 https://doi.org/10.1364/JOSA.70.001275	journal	January 1980
${}^{17}O$ nuclear-magnetic-resonance evidence for distinct carrier densities in the two types of ${CuO}_{2}$ planes of (Bi,Pb $)_{2}$ ${Sr}_{2}$ ${Ca}_{2}$ ${Cu}_{3}$ $O_{y}$ Trokiner, A.; Le Noc, L.; Schneck, J. Physical Review B, Vol. 44, Issue 5 https://doi.org/10.1103/PhysRevB.44.2426	journal	August 1991
Particle–hole symmetry breaking in the pseudogap state of Bi2201 Hashimoto, Makoto; He, Rui-Hua; Tanaka, Kiyohisa Nature Physics, Vol. 6, Issue 6 https://doi.org/10.1038/nphys1632	journal	April 2010
Evidence of a Precursor Superconducting Phase at Temperatures as High as 180 K in $R {Ba}_{2} {Cu}_{3} O_{7 - δ} (R = Y, Gd, Eu)$ Superconducting Crystals from Infrared Spectroscopy Dubroka, A.; Rössle, M.; Kim, K. W. Physical Review Letters, Vol. 106, Issue 4 https://doi.org/10.1103/PhysRevLett.106.047006	journal	January 2011
Optical conductivity and kinetic energy of the superconducting state: A cluster dynamical mean field study Haule, K.; Kotliar, G. Europhysics Letters (EPL), Vol. 77, Issue 2 https://doi.org/10.1209/0295-5075/77/27007	journal	January 2007
WHERE is the energy saved in cuprate superconductivity? Leggett, A. J. Journal of Physics and Chemistry of Solids, Vol. 59, Issue 10-12 https://doi.org/10.1016/S0022-3697(98)00091-2	journal	October 1998
Charge density wave fluctuations in ${La}_{2 - x}$ ${Sr}_{x}$ ${CuO}_{4}$ and their competition with superconductivity Croft, T. P.; Lester, C.; Senn, M. S. Physical Review B, Vol. 89, Issue 22 https://doi.org/10.1103/PhysRevB.89.224513	journal	June 2014
Theory of a Superfluid Fermi Liquid. I. General Formalism and Static Properties Leggett, A. J. Physical Review, Vol. 140, Issue 6A https://doi.org/10.1103/PhysRev.140.A1869	journal	December 1965
Doping dependence of the redistribution of optical spectral weight in ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$ Carbone, F.; Kuzmenko, A. B.; Molegraaf, H. J. A. Physical Review B, Vol. 74, Issue 6 https://doi.org/10.1103/PhysRevB.74.064510	journal	August 2006
Large Bi-2212 single crystal growth by the floating-zone technique Wen, J. S.; Xu, Z. J.; Xu, G. Y. Journal of Crystal Growth, Vol. 310, Issue 7-9 https://doi.org/10.1016/j.jcrysgro.2007.09.028	journal	April 2008
Nernst effect in high- $T_{c}$ superconductors Wang, Yayu; Li, Lu; Ong, N. P. Physical Review B, Vol. 73, Issue 2 https://doi.org/10.1103/PhysRevB.73.024510	journal	January 2006
Sum Rules and Interlayer Conductivity of High-Tc Cuprates Basov, D. N. Science, Vol. 283, Issue 5398 https://doi.org/10.1126/science.283.5398.49	journal	January 1999
Superconductivity-induced changes in density-density correlation function enabled by Umklapp processes Lee, Wei-Cheng Physical Review B, Vol. 91, Issue 22 https://doi.org/10.1103/PhysRevB.91.224503	journal	June 2015
Superconducting condensation energy and an antiferromagnetic exchange-based pairing mechanism Scalapino, D. J.; White, S. R. Physical Review B, Vol. 58, Issue 13 https://doi.org/10.1103/PhysRevB.58.8222	journal	October 1998
Some Thoughts About Two Dimensionality and Cuprate Superconductivity Leggett, Anthony J. Journal of Superconductivity and Novel Magnetism, Vol. 19, Issue 3-5 https://doi.org/10.1007/s10948-006-0154-y	journal	December 2006
Energetics of superconductivity in the two-dimensional Hubbard model Gull, E.; Millis, A. J. Physical Review B, Vol. 86, Issue 24 https://doi.org/10.1103/PhysRevB.86.241106	journal	December 2012
Interlayer Tunneling Mechanism for High-Tc Superconductivity: Comparison with c Axis Infrared Experiments Anderson, P. W. Science, Vol. 268, Issue 5214 https://doi.org/10.1126/science.268.5214.1154	journal	May 1995
Importance of phase fluctuations in superconductors with small superfluid density Emery, V. J.; Kivelson, S. A. Nature, Vol. 374, Issue 6521 https://doi.org/10.1038/374434a0	journal	March 1995
General trends in oxygen stoichiometry effects on Tc in Bi and Tl superconductors Presland, M. R.; Tallon, J. L.; Buckley, R. G. Physica C: Superconductivity, Vol. 176, Issue 1-3 https://doi.org/10.1016/0921-4534(91)90700-9	journal	May 1991