应变碳链中原子的非线性振动和结构相变
Nonlinear atomic vibrations and structural phase transitions in strained carbon chains
摘要：
本文研究了具有累积多烯结构（$=C=C=)_{n}$）的均匀应变碳链中原子的纵向非线性振动。借助基于密度泛函理论的从头算模拟，我们揭示了当应变超过临界值$η_{c}\approx 11\,{\%}$时，$π$模在一定幅度范围内的软化现象。这种软模的凝聚诱导碳链的结构转变，使其晶胞加倍。这是在应变累积多烯中的Peierls相变，其先前在[Nano Lett. 14，4224（2014）]。Peierls跃迁导致应变碳炔的电子能谱中出现能隙，使材料从导电态转变为半导体或绝缘态。上述论文的作者强调，这种现象可用于构建各种纳米器件。$π$模式软化的发生是因为旧的平衡位置（EQP），周围的碳原子振动在小的应变，失去了它们的稳定性，这些原子开始振动位于旧的EQP附近的新的势阱。我们研究了新的EQP的稳定性，以及在其附近的振动的稳定性。在先前的论文[Physica D 203，121（2005）]中，我们证明了在具有任意粒子间相互作用的单原子链中，只能存在三个由能量决定的Rosenberg非线性简正模。它们是上面讨论的$π$模式和两种其它模式，我们称之为$σ$模式和$τ$模式。与平衡态的晶胞相比，这些模式对应于振动态的晶胞的两倍、三倍或四倍的倍增。我们研究了具有任意粒子间相互作用对势的链模型中这些模的性质。
英文摘要：
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 $π$-mode softening in a certain range of its amplitude for the strain above the critical value $η_{c}\approx 11\,{\%}$. 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 $π$-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 $π$-mode and two other modes, which we call $σ$-mode and $τ$-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.
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