Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions
Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions
复制标题
DOI：
10.1002/pssb.201800524
复制
发表时间：
2019-01
期刊：
影响因子：
--
通讯作者：
T. Kawarabayashi;H. Aoki;Y. Hatsugai
中科院分区：
文献类型：
--
作者：
T. Kawarabayashi;H. Aoki;Y. Hatsugai
从理论上研究了二维晶格上无质量狄拉克费米子的倍增。研究表明，即使狄拉克锥体倾斜，手性对称性破缺晶格上的无质量狄拉克费米子的倍增也受到拓扑保护。这是由于晶格系统定义的广义手性对称性，其中此类模型可以通过手性对称晶格模型的变形来生成。本文表明，对于双能带晶格模型，这是产生具有广义手性对称性的系统的通用方法，因为此类系统总是可以转换回具有传统手性对称性的晶格模型。具体来说，它表明零模态的数量是变换的不变量，导致二维倾斜和无质量狄拉克费米子加倍的尼尔森-二宫拓扑保护。
The doubling of massless Dirac fermions on two‐dimensional lattices is theoretically studied. It has been shown that the doubling of massless Dirac fermions on a lattice with broken chiral symmetry is topologically protected even when the Dirac cone is tilted. This is due to the generalized chiral symmetry defined for lattice systems, where such models can be generated by a deformation of the chiral‐symmetric lattice models. The present paper shows for two‐band lattice models that this is a general way to produce systems with the generalized chiral symmetry in that such systems can always be transformed back to a lattice model with the conventional chiral symmetry. Specifically it is shown that the number of zero modes is an invariant of the transformation, leading to the topological protection à la Nielsen‐Ninomiya of the doubling of tilted and massless Dirac fermions in two dimensions.