  The precise driving force of the phase transition in indium nanowires on
Si(111) has been controversial whether it is driven by a Peierls instability or
by a simple energy lowering due to a periodic lattice distortion. The present
van der Waals (vdW) corrected hybrid density functional calculation predicts
that the low-temperature 8x2 structure whose building blocks are indium
hexagons is energetically favored over the room-temperature 4x1 structure. We
show that the correction of self-interaction error and the inclusion of vdW
interactions play crucial roles in describing the covalent bonding, band-gap
opening, and energetics of hexagon structures. The results manifest that the
formation of hexagons occurs by a simple energy lowering due to the lattice
distortion, not by a charge density wave formation arising from Fermi surface
nesting.
