  In scanning tunneling microscopy (STM) conductance curves, the
superconducting gap of cuprates is sometimes accompanied by small sub-gap
structures at very low energy. This was documented early on near vortex cores
and later at zero magnetic field. Using mean-field toy models of coexisting
d-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 this
phenomenon, with $s'$PDW playing a critical role. We explore the high
variability of the gap structure with changes in band structure and density
wave (DW) wave vector, thus explaining why sub-gap structures may not be a
universal feature in cuprates. In the absence of nesting, non-superconducting
results never show signs of pseudogap, even for large density waves magnitudes,
therefore reinforcing the idea of a distinct origin for the pseudogap, beyond
mean-field theory. Therefore, we also briefly consider the effect of DWs on a
pre-existing pseudogap.
