准周期链状聚合物电子谱及特征

准周期链状聚合物电子谱及特征 Electronic Spectrum and Wave Functions of Linear Polymers with Quasiperiodicity 朱家昆 ZHU Jia-kun 1 2 first-author 胡承正 HU Cheng-zheng 1 2 周详 ZHOU Xiang 1 2 龚平 GONG Ping 1 2 武汉大学物理科学与技术学院 武汉大学物理科学与技术学院 School of Physics and Technology,Wuhan University School of Physics and Technology,Wuhan University 武汉大学物理科学与技术学院,湖北,武汉,430072 武汉大学物理科学与技术学院,湖北,武汉,430072 研究了链状聚合物的长短键结构呈准周期排列的电子谱 .利用紧束缚近似和转移矩阵方法通过理论证明和计算表明 :这种准周期排列聚合物的电子谱 ,当长短键长度相差很小时 ,具有类似于金属晶体的能带结构 ;相差很大时 ,具有无序系统一维能级结构 ;而对于一般情形 ,其电子谱与上两者均异 ,形成所谓的类Cantor集 .这 3类不同的谱结构反映在链状聚合物的宏观物理性质上也将有所不同 ,它无疑会影响聚合物的稳定性及相关 （超 ）导电性能 ,深入研究这方面问题将有助于对有机超导的认识 . An investigation is given of linear polymers with quasiperiodicity, which can be regarded as intermediate between regular polymers and random systems. With a tight-binding model and transfer matrix calculation we study the electronic spectrum and wave fuctions of such polymers. The results show that:1) If the difference in length between the single and double bonds is small, the electronic spectrum and wave functions are similar to those of crystalline metals; 2) If the difference is large, the spectrum and wave functions are similar to those of random systems; 3) In general case, they are quite exotic: the energy spectrum is a Cartor set and the wave functions are "critical", i.e. neither localized nor extended. This three different spectrum structures would have influence on the macroscopic physical properties of linear polymers, such as stability, （super） conductivity. Further investigation in this field will help us to understanding organic superconductivity. 链状聚合物 准周期 电子谱 linear polymers quasiperiodicity the electronic spectrum O753.3 国家自然科学基金资助项目 （ 197740 44 ） 2003-03-01 2021-04-01 3