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

Abstract

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

6 pages with 3 color figures. Physical Review B, in press. For related papers, see http://www.prism.gatech.edu/~ph274cy/

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Cited by in corpus (9)

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• Dirac equation in curved spacetime: the role of local Fermi velocity
• Interplay of relativistic and nonrelativistic transport in atomically precise segmented graphene nanoribbons
• Classical and quantum dynamics of a kicked relativistic particle in a box
• Relativistic persistent currents in ideal Aharonov-Bohm rings
• Self-adjoint Dirac type Hamiltonians in one space dimension with a mass jump
• Relativistic currents on ideal Aharonov-Bohm cylinders
• Aharonov-Bohm rings in de Sitter expanding universe