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In scanning tunneling microscopy (STM) conductance curves, thesuperconducting gap of cuprates is sometimes accompanied by small sub-gapstructures at very low energy. This was documented early on near vortex coresand later at zero magnetic field. Using mean-field toy models of coexistingd-wave superconductivity ($d$SC), \emph{d}-form factor density wave ($d$FF-DW),and extended s-wave pair density wave ($s'$PDW), we find agreement with thisphenomenon, with $s'$PDW playing a critical role. We explore the highvariability of the gap structure with changes in band structure and densitywave (DW) wave vector, thus explaining why sub-gap structures may not be auniversal feature in cuprates. In the absence of nesting, non-superconductingresults never show signs of pseudogap, even for large density waves magnitudes,therefore reinforcing the idea of a distinct origin for the pseudogap, beyondmean-field theory. Therefore, we also briefly consider the effect of DWs on apre-existing pseudogap.

Density Waves Cause Sub-Gap Structures but no Pseudogap in Superconducting Cuprates