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The PnDOS of graphene (solid line). PnDOS when half of the carbon atoms are replaced with isotope 22 and 8 (dash and dotted-dash lines, respectively). The inset shows the arrangement of the regular carbon atoms (white) and the isotopes (black) in graphene lattice.
The PnDOS for substituted carbon atoms in graphene substituted with germanium when 1/6th and half of the atoms are replaced (solid and dash lines, respectively).
PnDOS of carbon atoms in graphene substituted with germanium when 4, 6, and 10 (solid, dash, and dotted lines, respectively) atoms are replaced out of a total of 16 atoms in the supercell.
The low and the high frequency of the gap (ωlow and ωhigh), the width (Δω = ωhigh − ωlow) over the mid-gap [ωg = (ωhigh + ωlow)/2] frequencies and the maximum frequency of the phonons (ωmax) for graphene with half of the carbon atoms having atomic mass A1 and the other half having atomic mass A2.
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