Determination of the superconducting gap sign by the phase referenced method: successful practice in cuprate and several iron based superconductors

In many unconventional superconductors, the superconducting gap will change sign along the Fermi surface. The fundamental reason for this behavior is that the Cooper pairing may be established through a repulsive interaction, instead of the attractive interaction in phonon mediated pairing picture. However to detect this gap sign is not easy at all. The usual method for solving this problem is to measure the behavior of phase difference or supercurrent through a Josephson junction. However, this method seems not working well in systems with multi-Fermi pockets and with the same sign in individual pocket. Such circumstances happen in many iron based superconductors.
In the superconducting state, quasi-particles (QPs) will be generated by thermal or pair breaking. These QPs with Bogoliubov dispersion are scattered from one momentum k₁ to another k₂ forming a standing wave with wave vector q=k₁-k₂. All these standing waves interfere each other and form a particular pattern in the real space (QPI). By using STM we can measure these patterns. Through the Fourier transform on QPI patterns we can not only get the Fermi surface contour, but also obtain the gap feature, including the magnitude and sign for different q vectors. This was called as the phase referenced QPI. Following this idea we have successfully detected the gap sign reversal in several iron based superconductors with and without the hole pockets. We can also directly visualize the d-wave gap in the typical cuprate superconductor Bi-2212.
References
1.Zengyi Du, Peter Hirschfield, Hai-Hu Wen et al., Nature Physics 14, 134(2018).
2.Qiangqiang Gu, Huan Yang, Hai-Hu Wen et al., Phys. Rev. B 98, 134503 (2018).
3.Mingyang Chen, Huan Yang, Qianghua Wang, Hai-Hu Wen et al. arXiv Condmat:1810.06414.
4.Qiangqiang Gu, Huan Yang, Hai-Hu Wen et al., arXiv Condmat:1808.06215.