Electron spin magnetism of zigzag graphene nanoribbon edge states

2014 ◽  
Vol 104 (16) ◽  
pp. 163104 ◽  
Author(s):  
Kun Xu ◽  
Peide D. Ye
Keyword(s):  
Electron Spin ◽  
Graphene Nanoribbon ◽  
Edge States ◽  
Spin Magnetism

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 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.

scholarly journals The family of topological Hall effects for electrons in skyrmion crystals

2018 ◽  
Vol 91 (8) ◽  
Author(s):  
Börge Göbel ◽  
Alexander Mook ◽  
Jürgen Henk ◽  
Ingrid Mertig
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Hall Effect ◽  
Electron Spin ◽  
Anomalous Hall Effect ◽  
Transverse Spin ◽  
Edge States ◽  
Finite Sample ◽  
Magnetic Texture ◽  
Hall Effects

Abstract Hall effects of electrons can be produced by an external magnetic field, spin–orbit coupling or a topologically non-trivial spin texture. The topological Hall effect (THE) – caused by the latter – is commonly observed in magnetic skyrmion crystals. Here, we show analogies of the THE to the conventional Hall effect (HE), the anomalous Hall effect (AHE), and the spin Hall effect (SHE). In the limit of strong coupling between conduction electron spins and the local magnetic texture the THE can be described by means of a fictitious, “emergent” magnetic field. In this sense the THE can be mapped onto the HE caused by an external magnetic field. Due to complete alignment of electron spin and magnetic texture, the transverse charge conductivity is linked to a transverse spin conductivity. They are disconnected for weak coupling of electron spin and magnetic texture; the THE is then related to the AHE. The topological equivalent to the SHE can be found in antiferromagnetic skyrmion crystals. We substantiate our claims by calculations of the edge states for a finite sample. These states reveal in which situation the topological analogue to a quantized HE, quantized AHE, and quantized SHE can be found.

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