  We present a generic grand-canonical theory for the Peierls transition in
atomic wires deposited on semiconducting substrates such as In/Si(111) using a
mean-field solution of the one-dimensional Su-Schrieffer-Heeger model. We show
that this simple low-energy effective model for atomic wires can explain
naturally the occurrence of a first-order Peierls transition between a uniform
metallic phase at high-temperature and a dimerized insulating phase at low
temperature as well as the existence of a metastable uniform state below the
critical temperature.
