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Open AccessArticle

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

Department of Physics, Korea University, Anam-dong 5, Seongbuk-gu, Seoul 02481, Korea
Nanomaterials 2019, 9(6), 885; https://doi.org/10.3390/nano9060885
Received: 20 May 2019 / Revised: 7 June 2019 / Accepted: 13 June 2019 / Published: 14 June 2019
(This article belongs to the Special Issue Nanotechnologies and Nanomaterials: Selected Papers from CCMR 2019)
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. View Full-Text
Keywords: chiral symmetry; fractional charge; topological insulator; soliton; graphene nanoribbon chiral symmetry; fractional charge; topological insulator; soliton; graphene nanoribbon
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Yang, S.-R.E. Soliton Fractional Charges in Graphene Nanoribbon and Polyacetylene: Similarities and Differences. Nanomaterials 2019, 9, 885.

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