Fig. 1: Water dissociation and proton transport at graphene electrodes.

a Schematic of graphene-electrode devices and our measurement setup. Green and blue balls represent hydrogen and oxygen atoms, respectively. Under strong electric field E, water molecules dissociate into H⁺ and OH⁻ pairs. OH⁻ drifts into the bulk electrolyte whereas H⁺ permeates through the graphene electrode, adsorbing on its external Pt-decorated surface and eventually recombining into molecular hydrogen. b Charge carrier density in graphene electrodes as a function of potential. The left (right) inset shows that for negative (positive) potentials, graphene is doped with electrons (holes). Solid lines, best linear fits. Dotted line marks a finite doping level at the neutrality point. Top x-axis, the Fermi energy μ_e in graphene (its electrochemical potential) extracted from Raman spectra. Electrolyte pH 7. c Examples of I–V characteristics in steady state conditions measured at different pH of the electrolyte (same 1 M KCl concentration). Top x-axis, corresponding μ_e. Arrows mark the zero-current potentials, φ, for each curve. d Zooming-in and comparing I–V responses obtained from graphene (red) and few-layer graphene (grey) electrodes in c.