scholarly journals Edge states of the long-range Kitaev chain: An analytical study

2020 ◽  
Vol 102 (3) ◽  
Author(s):  
Simon B. Jäger ◽  
Luca Dell'Anna ◽  
Giovanna Morigi
Keyword(s):  
Long Range ◽  
Analytical Study ◽  
Edge States

Edge states enhanced by long-range hopping: An analytical study

2021 ◽  
Author(s):  
Wang Hui-Ping ◽  
Ren li ◽  
Qin Liguo ◽  
Qiu Yueyin
Keyword(s):  
Long Range ◽  
Analytical Study ◽  
Edge States

scholarly journals Bulk-edge correspondence and long-range hopping in the topological plasmonic chain

Nanophotonics ◽  
2019 ◽  
Vol 8 (8) ◽  
pp. 1337-1347 ◽  
Author(s):  
Simon R. Pocock ◽  
Paloma A. Huidobro ◽  
Vincenzo Giannini
Keyword(s):  
Long Range ◽  
Metallic Nanoparticles ◽  
Nearest Neighbour ◽  
Edge States ◽  
Physical Treatment ◽  
Bulk Properties ◽  
One Dimensional ◽  
Measure Of Symmetry ◽  
Dipolar System ◽  
Desirable Trait

AbstractThe existence of topologically protected edge modes is often cited as a highly desirable trait of topological insulators. However, these edge states are not always present. A realistic physical treatment of long-range hopping in a one-dimensional dipolar system can break the symmetry that protects the edge modes without affecting the bulk topological number, leading to a breakdown in bulk-edge correspondence (BEC). Hence, it is important to gain a better understanding of where and how this occurs, as well as how to measure it. Here we examine the behaviour of the bulk and edge modes in a dimerised chain of metallic nanoparticles and in a simpler non-Hermitian next-nearest-neighbour model to provide some insights into the phenomena of bulk-edge breakdown. We construct BEC phase diagrams for the simpler case and use these ideas to devise a measure of symmetry-breaking for the plasmonic system based on its bulk properties. This provides a parameter regime in which BEC is preserved in the topological plasmonic chain, as well as a framework for assessing this phenomenon in other systems.

scholarly journals Tunable super- and subradiant boundary states in one-dimensional atomic arrays

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Anwei Zhang ◽  
Luojia Wang ◽  
Xianfeng Chen ◽  
Vladislav V. Yakovlev ◽  
Luqi Yuan
Keyword(s):  
Long Range ◽  
Quantum States ◽  
Two Dimensional ◽  
Edge States ◽  
Quantum Metrology ◽  
One Dimensional ◽  
Topological Quantum ◽  
Long Range Interactions ◽  
Boundary States ◽  
Quantum Optical

AbstractEfficient manipulation of quantum states is a key step towards applications in quantum information, quantum metrology, and nonlinear optics. Recently, atomic arrays have been shown to be a promising system for exploring topological quantum optics and robust control of quantum states, where the inherent nonlinearity is included through long-range hoppings. Here we show that a one-dimensional atomic array in a periodic magnetic field exhibits characteristic properties associated with an effective two-dimensional Hofstadter-butterfly-like model. Our work points out super- and sub-radiant topological edge states localized at the boundaries of the atomic array despite featuring long-range interactions, and opens an avenue of exploring an interacting quantum optical platform with synthetic dimensions.

scholarly journals Analytical study of the edge states in the bosonic Haldane model

2017 ◽  
Vol 29 (29) ◽  
pp. 295701 ◽  
Author(s):  
Pierre A Pantaleón ◽  
Y Xian
Keyword(s):  
Analytical Study ◽  
Edge States ◽  
Haldane Model

Analytical study of edge states in a semi-infinite graphene nanoribbon

2009 ◽  
Vol 80 (15) ◽  
Author(s):  
Liwei Jiang ◽  
Yisong Zheng ◽  
Cuishan Yi ◽  
Haidong Li ◽  
Tianquan Lü
Keyword(s):  
Analytical Study ◽  
Graphene Nanoribbon ◽  
Edge States
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