The non-Hermitian geometrical property of 1D Lieb lattice under Majorana’s stellar representation

doi:10.1088/1361-648X/ab9fd4

IMR OpenIR

	The non-Hermitian geometrical property of 1D Lieb lattice under Majorana’s stellar representation
	Xu,Xingran 1,2,3; Liu,Haodi 4; Zhang,Zhidong 1,2; Liang,Zhaoxin 3
	2020-07-23
发表期刊	Journal of Physics: Condensed Matter
ISSN	0953-8984
卷号	32 期号:42
摘要	AbstractThe topological properties of non-Hermitian Hamiltonian is a hot topic, and the theoretical studies along this research line are usually based on the two-level non-Hermitian Hamiltonian (or, equivalently, a spin-1/2 non-Hermitian Hamiltonian). We are motivated to study the geometrical phases of a three-level Lieb lattice model (or, equivalently, a spin-1 non-Hermitian Hamiltonian) with the flat band in the context of a polariton condensate. The topological invariants are calculated by both winding numbers in the Brillouin zone and the geometrical phase of Majorana stars on the Bloch sphere. Besides, we provide an intuitive way to study the topological phase transformation with the higher spin, and the flat band offers a platform to define the topological phase transition on the Bloch sphere. According to the trajectories of the Majorana stars, we calculate the geometrical phases of the Majorana stars. We study the Lieb lattice with a complex hopping and find their phases have a jump when the parameters change from the trivial phase to the topological phase. The correlation phase of Majorana stars will rise along with the increase of the imaginary parts of the hopping energy. Besides, we also study the Lieb lattice with different intracell hopping and calculate the geometrical phases of the model using non-Bloch factor under the Majorana’s stellar representation. In this case, the correlation phases will always be zero because of the normalized coefficient is always a purely real number and the phase transition is vividly shown with the geometrical phases of the Majorana stars calculated by the mean values of the total phases of both right and the joint left eigenstates.
关键词	non-Hermitian Majorana's stellar representation topological transition exciton–polariton skin effect
DOI	10.1088/1361-648X/ab9fd4
语种	英语
WOS记录号	IOP:0953-8984-32-42-ab9fd4
出版者	IOP Publishing
引用统计
文献类型	期刊论文
条目标识符	http://ir.imr.ac.cn/handle/321006/80664
专题	中国科学院金属研究所
作者单位	1.Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, People’s Republic of China 2.School of Materials Science and Engineering, University of Science and Technology of China, Hefei, 230026, People’s Republic of China 3.Department of Physics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China 4.Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, People’s Republic of China
推荐引用方式 GB/T 7714	Xu,Xingran,Liu,Haodi,Zhang,Zhidong,等. The non-Hermitian geometrical property of 1D Lieb lattice under Majorana’s stellar representation[J]. Journal of Physics: Condensed Matter,2020,32(42).
APA	Xu,Xingran,Liu,Haodi,Zhang,Zhidong,&Liang,Zhaoxin.(2020).The non-Hermitian geometrical property of 1D Lieb lattice under Majorana’s stellar representation.Journal of Physics: Condensed Matter,32(42).
MLA	Xu,Xingran,et al."The non-Hermitian geometrical property of 1D Lieb lattice under Majorana’s stellar representation".Journal of Physics: Condensed Matter 32.42(2020).