论文标题
在旋转不变的自旋弹性模型中屈曲
Buckling in a rotationally invariant spin-elastic model
论文作者
论文摘要
扫描隧道显微镜实验表明，在没有任何机械载荷的情况下，在加热的石墨烯片中自发的波纹到弯曲的过渡。已经提出了一些模型，这些模型依赖于弹性和内部，电子，自由度之间相互作用的图片，以理解这种现象。然而，这些模型并不完全与经典的弹性理论一致，因为它们不能保留旋转不变性。本文中，我们开发和分析了一种替代的经典自旋弹性模型，该模型可以保留旋转不变性，同时定性地说明了波纹到弯曲的过渡。通过整合内部自由度，得出了弹性模式的有效自由能，这仅取决于曲率。这种自由能的最小化导致了不同机械阶段的出现，这些机械阶段的热力学稳定性在分析和数值上都经过彻底分析。所有阶段均以空间均匀的曲率为特征，在一个和二维的情况下，在波纹到弯曲的过渡中扮演了顺序参数的作用。在后者中，我们的重点放在代表实际石墨烯的蜂窝晶格上。
Scanning tunneling microscopy experiments have revealed an 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 analyse 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. Minimisation of this free energy gives rise to the emergence of different mechanical phases, whose thermodynamic stability is thoroughly analysed, both analytically and numerically. All phases are characterised 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.
