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 ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{10+\ensuremath{\delta}}$ (Bi-2223), ferromagnetic iron pnictide ${\mathrm{EuRbFe}}_{4}{\mathrm{As}}_{4}$ (Eu-1144), and kagome metals $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=$ K, Rb, and Cs). Specifically, we explain the wave vectors, the particle-hole symmetry, and the dependence on the internal or external Zeeman-field of the coherence peak modulations. This paper 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.