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.
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