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

Abstract

Reproducible scanning tunneling microscope (STM) spectra of Bi2Sr2CaCu2O8+δ consistently exhibit asymmetric tunneling characteristics, with the higher peak conductance corresponding to a negatively biased sample. We consider various possible sources of this asymmetry that are not intrinsic to the superconducting state, including energy dependence of the normal-state densities of states of sample and/or tip, existence of bandwidth cutoffs, unequal work functions of tip and sample, and energy-dependent transmission probability. It is concluded that none of these effects can explain the sign and temperature dependence of the observed asymmetry. This indicates that the 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 will also give rise to a thermoelectric effect in STM experiments, resulting in a positive thermopower. We discuss the feasibility of observing this thermoelectric effect with an STM and conclude that it is easily observable. Again, contributions to this thermoelectric effect may also arise from energy dependence of normal-state densities of states and from energy-dependent transmission probability. However, because each of these features manifests itself differently in the thermoelectric effect and in the tunneling characteristics, an analysis of thermoelectric currents and voltages together with the tunneling spectra as a function of temperature and tip-sample distance would allow for accurate determination of the slope of the gap function. It is suggested that it would be very worthwhile to perform these experiments, because the slope of the gap function reflects a fundamental property of the superconducting state. In particular, the theory of hole superconductivity 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 existence of the gap slope discussed here.

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