Pair-breaking scattering interference as a mechanism for superconducting gap modulation

We propose the "pair-breaking scattering interference" as a general source of coherence peak modulations in superconductors. Assuming this mechanism, we present a simple physical picture for the coherence peak modulations in overdoped cuprate Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$ (Bi-2223), ferromagnetic iron pnictide EuRbFe$_4$As$_4$ (Eu-1144), and kagome metals $A$V$_3$Sb$_5$ ($A=$ K, Rb, and Cs). Specifically, we explain the wavevectors, the particle-hole symmetry, and the dependence on the internal or external Zeeman-field of the coherence peak modulations. This work is intended as a cautious reminder to the scientific community when asserting the existence of a pair density wave phenomenon in the absence of tunneling conductance modulations in the normal state.