Temperature-dependent ellipsometry measurements of partial Coulomb energy in superconducting cuprates

Abstract

We performed an experimental study of the temperature and doping dependence of the energy-loss function of the bilayer and trilayer Bi-cuprate 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 Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8-x}$ single crystals: under-doped with $T_c=60,70$ and 83K, optimally doped with $T_c=91$K, overdoped with $T_c=84,81,70$ and $58$K, as well as optimally doped Bi${}_2$Sr${}_2$Ca${}_2$Cu${}_3$O${}_{10+x}$ with $T_c=110$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. Due to the restriction to small momentum, our observations do not exclude a possible significant contribution to the condensation energy of the Coulomb energy associated to the region of $q$ around $(\pi ,\pi )$.

Revised version

References in corpus (15)

• Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8+d
• Resonant X-ray Scattering Study of Charge Density Wave Correlations in YBa${}_2$Cu${}_3$O${}_{6+x}$
• Appearance of fluctuating stripes at the onset of the pseudogap in the high-Tc Superconductor Bi2Sr2CaCu2O8+x
• Charge density wave fluctuations in La2-xSrxCuO4 and their competition with superconductivity
• Competing charge, spin, and superconducting orders in underdoped YBa2Cu3Oy
• Point nodes persisting far beyond Tc in Bi2212
• Energetics of superconductivity in the two dimensional Hubbard model
• Doping Dependence of the Redistribution of Optical Spectral Weight in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$
• An organizing principle for two-dimensional strongly correlated superconductivity
• Optical Conductivity of the t-J model within Cluster Dynamical Mean Field Theory
• Large Bi-2212 single crystal growth by the floating-zone technique
• Persistence of superconducting condensate far above the critical temperature in YBa${}_2$(Cu,Zn)${}_3$O${}_y$ revealed by $c$-axis optical conductivity measurements for several Zn concentrations and carrier doping levels
• In-plane optical spectral weight transfer in optimally doped Bi${}_2$Sr${}_2$Ca${}_2$Cu${}_3$O${}_{10}$
• Optical Integral in the Cuprates and the Question of Sum Rule Violation
• Superconductivity-Induced Changes in Density-Density Correlation Function Enabled by Umklapp Processes

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