Correlations among STM observables in disordered unconventional superconductors

Abstract

New developments in scanning tunneling spectroscopy now allow for the spatially resolved measurement of the Josephson critical current Ic between a tip and a superconducting sample, a nearly direct measurement of the true superconducting order parameter. However, it is unclear how these Ic measurements are correlated with previous estimates of the spectral gap taken from differential conductance measurements. In particular, recent experiments on an iron-based superconductor found almost no correlation between Ic and the spectral gap obtained from differential conductance g=dI/dV spectra, reporting instead a more significant correlation between Ic and the coherence-peak height. Here we point out that the correlation—or the lack thereof—between these various quantities can be naturally explained by the effect of disorder on unconventional superconductivity. Using large-scale numerical simulations of a BCS d-wave pair Hamiltonian with many-impurity potentials, we observe that “substitutional” disorder models with weak pointlike impurities lead to a situation in which the true superconducting order parameter and Ic are both uncorrelated with the spectral gap from dI/dV measurements and highly correlated with the coherence-peak heights. The underlying mechanism appears to be the disorder-induced transfer of spectral weight away from the coherence peaks. On the other hand, smooth impurity potentials with a length scale larger than the lattice constant lead to a large positive correlation between the true superconducting order parameter and the spectral gap, in addition to a large correlation between the order parameter and the coherence-peak height. We discuss the applicability of our results to recent Josephson scanning tunneling spectroscopy experiments on iron-based and cuprate high-temperature superconductors.

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