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 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 Bi_{2}Sr_{2}CaCu_{2}O_{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 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. 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).