  The structures and electron properties of new superlattices formed on
graphene by adsorbed hydrogen molecules are theoretically described. It has
been shown that superlattices of the (n, 0) zigzag type with linearly arranged
pairs of H atoms have band structures similar to the spectra of (n, 0) carbon
nanotubes. At the same time, superlattices of the (n, n) type with a
"staircase" of adsorbed pairs of H atoms are substantially metallic with a high
density of electronic states at the Fermi level and this property distinguishes
their spectra from the spectra of the corresponding (n, n) nanotubes. The
features of the spectra have the Van Hove form, which is characteristic of each
individual superlattice. The possibility of using such planar structures with
nanometer thickness is discussed.
