Correlations Among STM Observables in Disordered Unconventional Superconductors

TL;DR

This paper investigates how disorder affects correlations among various STM observables in unconventional superconductors, explaining experimental discrepancies through large-scale simulations of impurity effects on the superconducting order parameter.

Contribution

It demonstrates that impurity potential characteristics determine the correlation between the superconducting order parameter, spectral gap, and coherence-peak height in disordered unconventional superconductors.

Findings

Weak pointlike impurities cause uncorrelated order parameter and spectral gap, but correlated with coherence peaks.

Smooth impurity potentials lead to strong correlation between order parameter and spectral gap.

Disorder-induced spectral weight transfer explains experimental observations.

Abstract

New developments in scanning tunneling spectroscopy now allow for the spatially resolved measurement of the Josephson critical current $I_c$ between a tip and a superconducting sample, a nearly direct measurement of the true superconducting order parameter. However, it is unclear how these $I_c$ measurements are correlated with previous estimates of the spectral gap taken from differential conductance measurements. In particular, recent such experiments on an iron-based superconductor found almost no correlation between $I_c$ and the spectral gap obtained from differential conductance $g=dI/dV$ spectra, reporting instead a more significant correlation between $I_c$ and the 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 $I_c$ 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.