Measuring the Relative Phase of the Energy Gap in a High-Temperature   Superconductor with EELS
  A method of measuring the relative phase of the energy gap in a high-temperature superconductor is suggested for electron energy loss spectroscopy. Energy-resolved measurements of off-specular scattering should show a feature similar to the specular feature associated with the gap. Unlike the specular feature, which reflects an average of the gap over the (normal) Fermi surface, the energy loss of the off-specular feature depends on the superconducting energy gap at only two locations on the Fermi surface. The onset of the feature reflects the relative phase between these two points. This result is independent of surface characteristics. Such characteristics affect the {\it magnitude} of the off-specular feature, not its location or onset. The size of the feature is estimated for a simple surface model. Implications of specific measurements on $\rm Bi_2Sr_2CaCu_2O_8$ are discussed. 
Michael E. Flatte'