High-resolution electron-energy-loss study of the surfaces and energy gaps of cleaved high-temperature superconductors

High-resolution electron-energy-loss spectroscopy (HREELS) is used to characterize the resistivity, vibrational, and electronic structure of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$, and ${\mathrm{TiS}}_2$ single crystals cleaved in ultrahigh vacuum. The HREELS data are analyzed using dipole-scattering theory for a semi-infinite sequence of conducting sheets separated by dielectric slabs. Cleaved surfaces show strong lateral inhomogeneities and a variety of terminations with different properties. Spectroscopy on superconducting regions for a variety of these Cu-O–based superconductors reveals an energy gap in the ab plane that corresponds to (7.8±0.3)${\mathit{k}}_{\mathit{B}}$ ${\mathit{T}}_{\mathit{c}}$. The superconducting gap of the 1:2:3 material shows a non-BCS temperature dependence. We also analyze the infrared reflection data from the 1:2:3 material obtained by different groups and find good agreement with our HREELS results. Based on these experimental results, we suggest that the transition to superconductivity is due to a Bose-Einstein condensation of the preexisting or ‘‘real’’ space pairs.