Title: Nonlinear atomic vibrations and structural phase transitions in strained carbon chains,
Abstract: We consider longitudinal nonlinear atomic vibrations in uniformly strained
carbon chains with the cumulene structure ($=C=C=)_{n}$. With the aid of ab
initio simulations, based on the density functional theory, we have revealed
the phenomenon of the $\pi$-mode softening in a certain range of its amplitude
for the strain above the critical value $\eta_{c}\approx 11\,{\%}$.
Condensation of this soft mode induces the structural transformation of the
carbon chain with doubling of its unit cell. This is the Peierls phase
transition in the strained cumulene, which was previously revealed in [Nano
Lett. 14, 4224 (2014)]. The Peierls transition leads to appearance of the
energy gap in the electron spectrum of the strained carbyne, and this material
transforms from the conducting state to semiconducting or insulating states.
The authors of the above paper emphasize that such phenomenon can be used for
construction of various nanodevices. The $\pi$-mode softening occurs because
the old equilibrium positions (EQPs), around which carbon atoms vibrate at
small strains, lose their stability and these atoms begin to vibrate in the new
potential wells located near old EQPs. We study the stability of the new EQPs,
as well as stability of vibrations in their vicinity. In previous paper
[Physica D 203, 121(2005)], we proved that only three symmetry-determined
Rosenberg nonlinear normal modes can exist in monoatomic chains with arbitrary
interparticle interactions. They are the above-discussed $\pi$-mode and two
other modes, which we call $\sigma$-mode and $\tau$-mode. These modes
correspond to the multiplication of the unit cell of the vibrational state by
two, three or four times compared to that of the equilibrium state. We study
properties of these modes in the chain model with arbitrary pair potential of
interparticle interactions.