二维狄拉克费米子及其拓扑态  

2-D Dirac Fermion and Its Topological States

作　　者：邢燕霞[1] 梁钰林 XING Yanxia;LIANG Yulin(School of Physics,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]北京理工大学物理学院,北京100081

出　　处：《山西大学学报（自然科学版）》2022年第3期672-692,共21页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(12174023)。

摘　　要：用能带理论的语言说明何谓拓扑相变、如何用拓扑不变量表示拓扑相变;选取简单而富含物理的二能级系统,求解实际系统的拓扑不变量,展示二能级拓扑相变和倒空间单极点的等价性;进一步通过参数映射,结合单极点模型,说明如何在不计算拓扑不变量的前提下,通过z方向赝自旋分布,快速判断二能级系统是否发生拓扑相变;最后,选取三类典型材料:石墨烯、拓扑绝缘体、外尔半金属,展示并验证此简单判据的有效性。This article uses language of band theory to explain what is topological phase transition and how to characterize topological phase transition by topological invariant.The article chooses two-level system which is simple but rich in physics to solve reality systems’topological invariant and shows the equivalence of two-level topological phase transition and monopoles in reciprocal space.Furthermore,via parameter reflecting along with monopole model,the article explains by pseudo-spin’s z component distribution how to quickly tell if topological phase transition takes place in a two-level system in the premise that there is no need to calculate the topological invariant.At last,the article chooses three kinds of representative materials:graphene,topological insulator and Weyl semi-metal to display and verify the effectiveness of brief criterion.

关 键 词：拓扑绝缘体 石墨烯 狄拉克费米子 拓扑陈数 拓扑边缘态 

分 类 号：O469[理学—凝聚态物理]