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

TL;DR

This paper explores topological states and relativistic particle analogies in graphene nanorings with different edge terminations, revealing novel quantum behaviors and topological effects beyond the massless Dirac fermion model.

Contribution

It introduces a relativistic Dirac-Kronig-Penney model analysis to describe topological states in graphene nanorings, highlighting position-dependent mass and symmetry-breaking effects.

Findings

Armchair hexagonal rings exhibit ultrarelativistic fermion behavior with position-dependent mass.

Zigzag hexagonal rings correspond to nonrelativistic massive fermions at low kinetic energy.

Topological effects are linked to edge terminations and symmetry-breaking in the system.

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.