are described by thermodynamic cycles (see SI for details on partial reactions and details). Both reactions are strongly endothermic with overall 2.18 eV for the transfer of a proton and 2.54 eV for the transfer of an H atom from the PdH x electrodes to h-BN. This rough estimate mainly serves to illustrate the expectation that it is much more favorable for a proton to enter the layered material. It is interesting to note that the protium recombination in the lattice, calculated to be 3.46 eV, would lower the energy by 1.73 eV per atom, resulting in 0.81 eV per atom. The full thermodynamic simulation of the process of proton/protium transfer in the device is beyond our present capabilities and requires more detailed atomistic information about the interface from the experiment.