Surface state effects in high-Tcsuperconductors

All copper oxide based high-${\mathit{T}}_{\mathit{c}}$ superconductors share the common property that the c-axis coherence length is shorter than the lattice repeat distance in the same direction. In a semi-infinite system whose top surface is an ab plane, the superconducting properties near the surface may be drastically affected. We report in this paper detailed analyses of the surface properties of model layered superconductors with one and two layers in a unit cell. We have found that for the one-layer model the change in surface electronic structure has no effect on the critical temperature ${\mathit{T}}_{\mathit{c}}$ and the order parameter Δ. For a two-layer model with one superconducting (S) layer and one normal (N) layer, the order parameter of the top S layer is generally larger than that of the bulk. The enhancement effect is particularly large when a band of surface state exists on the top S layer. In this event, the energy gap structure measured by the point-contact tunneling technique is expected to be very different from that measured by the junction tunneling technique. Such differences have been reported for ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathrm{\delta }}$ and ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$. The existence of a surface band also adds complications to the interpretation of the photoemission measurements of the superconducting energy gap, to the extent that the observed gap anisotropy may actually reflect the uneven distribution of the spectral weight of the surface state on the top layer. How to extend these findings to systems with three and more layers in a unit cell will also be discussed.