Topological effects and particle-physics analogies beyond the massless Dirac-Weyl fermion in graphene nanorings

Abstract

Armchair and zigzag edge terminations in planar hexagonal and trigonal graphene nanorings are shown to underlie one-dimensional topological states associated with distinctive energy gaps and patterns (e.g., linear dispersion of the energy of an hexagonal ring with an armchair termination versus parabolic dispersion for a zigzag terminated one) in the bands of the tight-binding spectra as a function of the magnetic field. A relativistic Dirac-Kronig-Penney model analysis of the tight-binding Aharonov-Bohm behavior reveals that the graphene quasiparticle in an armchair hexagonal ring is a condensed-matter realization of an ultrarelativistic fermion with a position-dependent mass term, akin to the zero-energy fermionic solitons with fractional charge familiar from quantum field theory and from the theory of polyacetylene. The topological origins of the above behavior are highlighted by contrasting it with the case of a trigonal armchair ring, where we find that the quasiparticle excitations behave as familiar Dirac fermions with a constant mass. Furthermore, the spectra of a zigzag hexagonal ring correspond to the low-kinetic-energy nonrelativistic regime of a leptonlike massive fermion. A onedimensional relativistic Lagrangian formalism coupling a fermionic and a scalar bosonic field via a Yukawa interaction, in conjunction with the breaking of the Z2 reflectional symmetry of the scalar field, is shown to unify the above dissimilar behaviors.

arXiv comment12 pages with 10 color figures. For related papers, see http://www.prism.gatech.edu/~ph274cy/ For a version with high-quality figures, see http://www.prism.gatech.edu/~ph274cy/

References in corpus (28)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Energy Gaps in Graphene Nanoribbons
• Chiral tunneling and the Klein paradox in graphene
• Quantum properties of atomic-sized conductors
• Electronic States of Graphene Nanoribbons
• New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials
• Analytical Study of Electronic Structure in Armchair Graphene Nanoribbons
• Aharonov-Bohm effect and broken valley-degeneracy in graphene rings
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• Edge States and the Quantized Hall Effect in Graphene
• Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator
• Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
• Dirac and Klein-Gordon particles in one-dimensional periodic potentials
• Engineering artificial graphene in a two-dimensional electron gas
• Inner and outer edge states in graphene rings: A numerical investigation
• Simplified model for the energy levels of quantum rings in single layer and bilayer graphene
• Energetics, forces, and quantized conductance in jellium modeled metallic nanowires
• The Aharonov-Bohm effect in graphene rings
• Spectrum of $\pi$ Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance
• Dirac Spectrum in Piecewise Constant One-Dimensional Potentials
• Manipulating atoms in an optical lattice: Fractional fermion number and its optical quantum measurement
• Effective Time Reversal Symmetry Breaking and Energy Spectra of Graphene Armchair Rings
• Fractional and Majorana Fermions: The Physics of Zero Energy Modes
• Peierls Instability in Carbon Nanotubes
• Patterns of the Aharonov-Bohm oscillations in graphene nanorings
• Particle number fractionalization of a one-dimensional atomic Fermi gas with synthetic spin-orbit coupling
• Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior

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• Mass-profile quantum dots in graphene
• Topological insulator ring with magnetic impurities
• Quantum vacuum fluctuation effects in a quasi-periodically identified conical spacetime
• Dirac electrons in quantum rings
• Chiral properties of topological-state loops
• Interplay of relativistic and nonrelativistic transport in atomically precise segmented graphene nanoribbons
• Lorentz Violation and Topologically Trapped Charge Carriers in 2D Materials
• Signature of topological phases in Zitterbewegung