# Robustness of Quasiparticle Interference Test for Sign-changing Gaps in Multiband Superconductors

## TL;DR

This paper examines the robustness of a quasiparticle interference test for detecting sign-changing gaps in multiband superconductors, showing it is reliable with isolated impurities but less so with multiple dilute impurities.

## Contribution

The study demonstrates that the quasiparticle interference test remains effective for sign-changing gaps when impurities are isolated, despite challenges with multiple dilute impurities.

## Key findings

- Single impurity results are exact and reliable.
- Multiple dilute impurities complicate the interpretation.
- Isolating a single impurity restores the test's effectiveness.

## Abstract

Recently, a test for a sign-changing gap function in a candidate multiband unconventional superconductor involving quasiparticle interference data was proposed. The test was based on the antisymmetric, Fourier transformed conductance maps integrated over a range of momenta $\bf q$ corresponding to interband processes, which was argued to display a particular resonant form, provided the gaps changed sign between the Fermi surface sheets connected by $\bf q$. The calculation was performed for a single impurity, however, raising the question of how robust this measure is as a test of sign-changing pairing in a realistic system with many impurities. Here we reproduce the results of the previous work within a model with two distinct Fermi surface sheets, and show explicitly that the previous result, while exact for a single nonmagnetic scatterer and also in the limit of a dense set of random impurities, can be difficult to implement for a few dilute impurities. In this case, however, appropriate isolation of a single impurity is sufficient to recover the expected result, allowing a robust statement about the gap signs to be made.