常曲率二维弯曲系统中KT相变的理论研究

Kosterlitz-Thouless phase transition (KT phase transition) is a type of topological phase transition. It is a key problem of the studies of thermal characteristics in 2D system. However, in curved 2D material of which surface have constant curvature, such as fullerenes and carbon nanotubes, the researches of KT phase transition are lack. It is necessary to develop the KTHNY theory in plane system to the 2D curved system. This program includes three aspects: (1) by the KTHNY theory in plane system, the corresponding theory in 2D curved system is established, while the effect of curvature about the KT phase transition will be studied; (2) the influence of the boundary, deformation and inherent defects on the KT phase transition of 2D curved system will be involved; (3) for the two-dimensional structure materials, such as fullerenes and carbon nanotubes, the melting temperature which is difficult to be determined accurately will be derived by our theory. Then, comparing to the simulation and experimental studies, we will inspect and correct the established theory. This program will reveal the characteristics of the KT phase transition on the 2D curved system with constant curvature, and promote the usage of functional materials and nano-devices.

Kosterlitz-Thouless相变（KT相变）为二维系统中的拓扑相变，是二维系统热学特性研究的关键问题之一，然而关于富勒烯、碳纳米管等常曲率二维结构材料KT相变的研究还存在空白，因此有必要推广和发展平面系统KTHNY理论到二维弯曲系统中。本项目的研究内容包括三个方面：(1)借鉴平面系统KTHNY理论，建立具有常曲率的二维弯曲系统中的相应理论，研究曲率对系统KT相变的影响；(2)研究边界、形变、固有缺陷等因素影响弯曲系统KT相变的微观机制；(3)以具体材料为例（如富勒烯、碳纳米管），对所建立的理论进行检验和修正，并在此基础上尝试解决二维结构材料熔化温度难以被精确确定的问题。本研究将揭示常曲率二维弯曲系统的KT相变特性，为功能材料和纳米器件的设计及应用提供理论依据。

Kosterlitz-Thouless相变（KT相变）属于拓扑相变，是二维系统热学特性研究的关键问题之一。KT相变可存在于XY 模型、固液相变及中性超导体等二维结构中，然而二维弯曲系统中是否存在KT相变的研究还存在空白。本项目建立了二维弯曲系统中的KTHNY理论，给出了柱面、球面系统的相变温度。另外，碳基材料二维材料具有很高的应用前景和实用价值，然而由于实验水平的限制，碳纳米管的熔化温度还无法准确测量，且现有的数值模拟结果差异较大，而二维弯曲系统KTHNY理论提供了分析碳纳米管熔化过程的理论支持。借助该理论，我们推导出了碳纳米管的熔化温度，并分析给出了边界、固有缺陷和弯曲形变对相变的影响。通过理论和模拟计算对比分析，发现弯曲形变会促进相变发生；存在固有缺陷时熔化温度会升高；边界附近易成为相变的起始点；而手性对碳纳米管的熔化温度没有影响。本研究揭示了二维弯曲系统的KT相变特性，为功能材料和纳米器件的设计及应用提供了理论依据。