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

doi:10.1088/1361-648X/ab9fd4

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	The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation
	Xu, Xingran 1,2,5; Liu, Haodi 3,4; Zhang, Zhidong 1,2; Liang, Zhaoxin 5
刊名	JOURNAL OF PHYSICS-CONDENSED MATTER
	2020-10-07
卷号	32 期号:42 页码:12
关键词	non-Hermitian Majorana's stellar representation topological transition exciton-polariton skin effect
ISSN号	0953-8984
DOI	10.1088/1361-648X/ab9fd4
通讯作者	Liang, Zhaoxin(zhxliang@gmail.com)
英文摘要	The 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.
资助项目	National Natural Science Foundation of China[11604300] ; National Natural Science Foundation of China[11875103] ; Key Projects of the Natural Science Foundation of China[11835011] ; NSFC of China[51331006]
WOS研究方向	Physics
语种	英语
出版者	IOP PUBLISHING LTD
WOS记录号	WOS:000555812300001
资助机构	National Natural Science Foundation of China ; Key Projects of the Natural Science Foundation of China ; NSFC of China
内容类型	期刊论文
源URL	[http://ir.imr.ac.cn/handle/321006/140109]
专题	金属研究所_中国科学院金属研究所
通讯作者	Liang, Zhaoxin
作者单位	1.Univ Sci & Technol China, Sch Mat Sci & Engn, Hefei 230026, Peoples R China 2.Chinese Acad Sci, Inst Met Res, Shenyang Natl Lab Mat Sci, Shenyang 110016, Peoples R China 3.Northeast Normal Univ, Sch Phys, Changchun 130024, Peoples R China 4.Northeast Normal Univ, Ctr Quantum Sci, Changchun 130024, Peoples R China 5.Zhejiang Normal Univ, Dept Phys, Jinhua 321004, Zhejiang, Peoples R China
推荐引用方式 GB/T 7714	Xu, Xingran,Liu, Haodi,Zhang, Zhidong,et al. The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation[J]. JOURNAL OF PHYSICS-CONDENSED MATTER,2020,32(42):12.
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),12.
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):12.