  The superconducting state of metals has long provided a classic example of
particle-hole symmetry (PHS) at low energy. Fermionic self-energy results based
on first principles theory for the electron-phonon coupling in H$_3$S presented
here illustrate strong PHS-breaking dynamics arising from the underlying sharp
structure in the fermionic density of states. Thus H$_3$S is not only the
superconductor with the highest critical temperature $T_c$ (through 2018), but
its low energy, low temperature properties deviate strongly from textbook
behavior. The minor momentum and band dependence of the fermionic self-energy
allows evaluation of the momentum-resolved and zone-averaged spectral densities
and interacting thermal distribution function, all of which clearly illustrate
strong particle-hole asymmetry.
