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

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

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

scholarly journals Soliton Fractional Charges in Graphene Nanoribbon and Polyacetylene: Similarities and Differences

Nanomaterials ◽  
2019 ◽  
Vol 9 (6) ◽  
pp. 885 ◽  
Author(s):  
S.-R. Eric Yang
Keyword(s):  
Domain Wall ◽  
Graphene Nanoribbons ◽  
Coupling Effect ◽  
Scalar Potential ◽  
Graphene Nanoribbon ◽  
Antiferromagnetic Coupling ◽  
Fermion Mass ◽  
Edge States ◽  
Chiral Soliton ◽  
Charge Fractionalization

An introductory overview of current research developments regarding solitons and fractional boundary charges in graphene nanoribbons is presented. Graphene nanoribbons and polyacetylene have chiral symmetry and share numerous similar properties, e.g., the bulk-edge correspondence between the Zak phase and the existence of edge states, along with the presence of chiral boundary states, which are important for charge fractionalization. In polyacetylene, a fermion mass potential in the Dirac equation produces an excitation gap, and a twist in this scalar potential produces a zero-energy chiral soliton. Similarly, in a gapful armchair graphene nanoribbon, a distortion in the chiral gauge field can produce soliton states. In polyacetylene, a soliton is bound to a domain wall connecting two different dimerized phases. In graphene nanoribbons, a domain-wall soliton connects two topological zigzag edges with different chiralities. However, such a soliton does not display spin-charge separation. The existence of a soliton in finite-length polyacetylene can induce formation of fractional charges on the opposite ends. In contrast, for gapful graphene nanoribbons, the antiferromagnetic coupling between the opposite zigzag edges induces integer boundary charges. The presence of disorder in graphene nanoribbons partly mitigates antiferromagnetic coupling effect. Hence, the average edge charge of gap states with energies within a small interval is e / 2 , with significant charge fluctuations. However, midgap states exhibit a well-defined charge fractionalization between the opposite zigzag edges in the weak-disorder regime. Numerous occupied soliton states in a disorder-free and doped zigzag graphene nanoribbon form a solitonic phase.

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