In conclusion, both H + and H atom can diffuse easily through the interstitial space of layered materials h-BN and MoS 2 , while they are immobile in graphite. The overall lattice of the layered materials remains intact. Locally, protons bind to N (S for MoS 2 ), pick an electron from the lattices and leave a charged site that extends over a few atoms. At low concentration, this charged state will be maintained. Protons could be transported between the layers of such 2D materials due to the Coulomb repulsion between the protons and the electric field gradient between the electrodes. On the other hand, protiums will bind to B (S for MoS 2 ) atoms. If two protiums are getting close, they will form proton-hydride pairs, and at high concentration, they will recombine to H 2 . Thus, for low concentration, both pathways are in principle possible. In both carrier materials, the transport process is supported by the shear modes of the material and follows a hopping process between neighboring layers. Our results should be of interest for hydrogen transport in other layered van der Waals materials, which could be important for applications, such as hydrogen isotope separation or proton exchange membranes.