Electronic properties of a graphene antidot in magnetic fields

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

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.

Bandgap opening in graphene antidot lattices: the missing half

The electronic structure of graphene antidot lattices (GALs) with zigzag hole edges was studied with first-principles calculations. It was revealed that half of the possible GAL patterns were unintentionally missed in the usual construction models used in earlier studies. With the complete models, the bandgap of the GALs was sensitive to the width W of the wall between the neighboring holes. A nonzero bandgap was opened in hexagonal GALs with even W, while the bandgap remained closed in those with odd W. Similar alternating gap opening/closing with W was also demonstrated in rhombohedral GALs. Moreover, analytical solutions of single-walled GALs were derived based on a tight-binding model to determine the location of the Dirac points and the energy dispersion, which confirmed the unique effect in GALs.