Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain.
Phys Rev E. 2023 Jan;107(1-1):014120. doi: 10.1103/PhysRevE.107.014120.
Scanning tunneling microscopy experiments have revealed a spontaneous rippled-to-buckled transition in heated graphene sheets, in absence of any mechanical load. Several models relying on a simplified picture of the interaction between elastic and internal, electronic, degrees of freedom have been proposed to understand this phenomenon. Nevertheless, these models are not fully consistent with the classical theory of elasticity, since they do not preserve rotational invariance. Herein, we develop and analyze an alternative classical spin-elastic model that preserves rotational invariance while giving a qualitative account of the rippled-to-buckled transition. By integrating over the internal degrees of freedom, an effective free energy for the elastic modes is derived, which only depends on the curvature. Minimization of this free energy gives rise to the emergence of different mechanical phases, whose thermodynamic stability is thoroughly analyzed, both analytically and numerically. All phases are characterized by a spatially homogeneous curvature, which plays the role of the order parameter for the rippled-to-buckled transition, in both the one- and two-dimensional cases. In the latter, our focus is put on the honeycomb lattice, which is representative of actual graphene.
扫描隧道显微镜实验揭示了在没有任何机械负载的情况下，加热的石墨烯片会自发地发生从波纹到褶皱的转变。为了理解这一现象，已经提出了几个依赖于弹性和内部电子自由度之间简化相互作用模型的模型。然而，这些模型与弹性力学的经典理论不完全一致，因为它们不保持旋转不变性。在这里，我们开发并分析了一种替代的经典自旋弹性模型，该模型在保持旋转不变性的同时，对波纹到褶皱的转变给出了定性的解释。通过对内部分度自由度进行积分，推导出了弹性模式的有效自由能，该自由能仅取决于曲率。这个自由能的最小化导致了不同力学相的出现，我们对它们的热力学稳定性进行了深入的分析，包括解析和数值分析。所有的相都具有空间均匀的曲率，在一维和二维情况下，它都起着波纹到褶皱转变的序参量的作用。在后者中，我们的重点是蜂窝晶格，它代表了实际的石墨烯。
