A longstanding mystery in understanding cuprate superconductors is the inconsistency between
the experimental data measured by scanning tunneling spectroscopy (STS) and angle-resolved
photoemission spectroscopy (ARPES). In particular, the gap between prominent side peaks observed
in STS is much bigger than the superconducting gap observed by ARPES measurements. Here, we
reconcile the two experimental techniques by generalising a theory which was previously applied
to zero-dimensional mesoscopic Kondo systems to strongly correlated two-dimensional (2D) exotic
superconductors. We show that the side peaks observed in tunneling conductance measurements in all
these materials have a universal origin: They are formed by coherence-mediated tunneling under bias
and do not directly reflect the underlying density of states (DOS) of the sample. We obtain theoretical
predictions of the tunneling conductance and the density of states of the sample simultaneously and
show that for cuprate and pnictide superconductors, the extracted sample DOS is consistent with the
superconducting gap measured by ARPES.