  Density-functional calculations are used to verify the atomic structure of
the hexagonal In/Si(111)-($\sqrt{7}\times\sqrt{3}$) surface, which has been
considered to represent an ultimate two-dimensional (2D) limit of metallic In
overlayers. Contrary to the prevailing assumption, this surface consists of not
a single layer but a double layer of In atoms, which corresponds to a hexagonal
deformation of the well-established $rectangular$ In double layer formed on
Si(111)-($\sqrt{7}\times\sqrt{3}$) [Park $et$ $al$., Phys. Rev. Lett. 109,
166102 (2012)]. The same double-layer thickness accounts well for the typical
coexistence of the hexagonal and rectangular phases and their similar 2D
electronic structures. It is thus conclusive that, regardless of rectangular or
hexagonal, the In/Si(111)-($\sqrt{7}\times\sqrt{3}$) surface does not represent
an one-atom-thick In overlayer.
