Slope of the superconducting gap function in Bi2Sr2CaCu2O8+delta measured by vacuum tunneling spectroscopy

Reproducible scanning tunneling microscope (STM) spectra of Bi2Sr2CaCu2O8+d elta consistently exhibit asymmetric tunneling characteristics, with the hi gher peak conductance corresponding to a negatively biased sample. We consi der various possible sources of this asymmetry that are not intrinsic to th e superconducting state, including energy dependence of the normal-state de nsities of states of sample and/or tip, existence of bandwidth cutoffs, une qual work functions of tip and sample, and energy-dependent transmission pr obability. It is concluded that none of these effects can explain the sign and temperature dependence of the observed asymmetry. This indicates that t he observed asymmetry reflects an intrinsic property of the superconducting state: an energy-dependent superconducting gap function with nonzero slope at the Fermi energy. It is pointed out that such a sloped gap function wil l also give rise to a thermoelectric effect in STM experiments, resulting i n a positive thermopower. We discuss the feasibility of observing this ther moelectric effect with an STM and conclude that it is easily observable. Ag ain, contributions to this thermoelectric effect may also arise from energy dependence of normal-state densities of states and from energy-dependent t ransmission probability. However, because each of these features manifests itself differently in the thermoelectric effect and in the tunneling charac teristics, an analysis of thermoelectric currents and voltages together wit h the tunneling spectra as a function of temperature and tip-sample distanc e would allow for accurate determination of the slope of the gap function. It is suggested that it would be very worthwhile to perform these experimen ts, because the slope of the gap function reflects a fundamental property o f the superconducting state. In particular, the theory of hole superconduct ivity has predicted the existence of such a slope, of universal sign,in all superconductors. It is furthermore argued that recent experimental results on vortex lattice imaging provide further strong evidence for the existenc e of the gap slope discussed here. [S0163-1829(99)04118-1].