Surface State Effects in High-TcSuperconductors

Under appropriate conditions a band of electronic surface states may exist on the topmost Cu${\mathrm{O}}_2$ layer of a high-$T_c$ superconductor. This layer can then have higher $T_c$ and energy gap values than the bulk. The surface band vanishes at the $k_x$, $k_y$ points in the Brillouin zone where the bulk bands touch. Such surface states can cause tunneling results to depend upon the method and the geometry, and alter the interpretation of photoemission measurements of the energy gap. Both experiments are consistent with $s$-wave order parameter symmetry in high-$T_c$ materials.