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The doubly-connected polygonal geometry of planar graphene rings is found tobring forth topological configurations for accessing nontrivial relativisticquantum field (RQF) theory models that carry beyond the constant-massDirac-fermion theory. These include generation of sign-alternating masses,solitonic excitations, and charge fractionization. The work integrates a RQFLagrangian formulation with numerical tight-binding Aharonov-Bohm electronicspectra and the generalized position-dependent-mass Dirac equation. In contrastto armchair graphene rings (aGRGs) with pure metallic arms, certain classes ofaGRGs with semiconducting arms, as well as with mixed metallic-semiconductingones, are shown to exhibit properties of one-dimensional nontrivial topologicalinsulators. This further reveals an alternative direction for realizing agraphene-based nontrivial topological insulator through the manipulation of thehoneycomb lattice geometry, without a spin-orbit contribution.

Beyond the constant-mass Dirac physics: Solitons, charge fractionization, and the emergence of topological insulators in graphene rings