This sounds promising but don't quite fully understand its explanation of how it works.
"...During charging, the carbon in the electrode bonds with protons generated by splitting water..."
Protons are hydrogen nuclei.
When they say the carbon 'bonds' with protons, do they mean 'bonds' as in forming covalent bonds so to change the carbon into hydrocarbon and with an electron orbital around each proton?
If so, because of the Gibbs function in relation to chemical bonds, I would be surprised if it could have much energy density.
Or do they mean some kind of ionic bond with the carbon so that no electron orbitals around each proton?
If so, how on earth can that work when carbon doesn't readily form ionic bonds?