Zone-center gap in the frequency spectrum of a commensurate monolayer

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Abstract
The gap at the Brillouin-zone center in the frequency spectrum of small-amplitude vibrations of a commensurate-monolayer solid is expressed in terms of the leading Fourier amplitudes of the atom-substrate potential. Cases with one atom per unit cell, e.g., a commensurate lattice of krypton on graphite, and with four atoms per unit cell, e.g., a commensurate lattice of neon on graphite, are treated.