Majorana Fermions in Honeycomb Lattices

Abstract

We study the formation of Majorana fermions in honeycomb-lattice structures in the presence of a Zeeman field, Rashba spin-orbit coupling, and in the proximity of an s-wave superconductor. We show that an exact mapping exists between an anisotropic hexagonal-lattice nanoribbon at k = 0 and a one-dimensional chain, for which the existence of Majorana fermions has been extensively discussed. Consequently we can predict the conditions for the emergence of Majorana fermions at the edges of such ribbon, and relate the existence of Majoranas to a band inversion in the bulk band structure. Moreover we find that similar situations arise in isotropic lattices and we give some examples which show the formation of Majorana fermions in these structures.

7 pages, 9 figures

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Cited by in corpus (24)

• Fermionic and Majorana Bound States in Hybrid Nanowires with Non-Uniform Spin-Orbit Interaction
• Visualising Majorana bound states in 1D and 2D using the generalized Majorana polarization
• Majorana bound states in open quasi-1D and 2D systems with transverse Rashba coupling
• Majorana bound states in semiconducting nanostructures
• Flat Majorana bands in 2-d lattices with inhomogeneous magnetic fields: topology and stability
• Majorana and parafermion corner states from two coupled sheets of bilayer graphene
• Suppression of the overlap between Majorana fermions by orbital magnetic effects in semiconducting-superconducting nanowires
• Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons
• On the bulk boundary correspondence and the existence of Majorana bound states on the edges of 2D topological superconductors
• Topological edge states on time-periodically strained armchair graphene nanoribbons
• Prevalence of trivial zero-energy sub-gap states in non-uniform helical spin chains on the surface of superconductors
• Chiral Majorana fermions in graphene from proximity-induced superconductivity
• Formation of Majorana fermions in finite-size graphene strips
• Majorana bound states in germanium Josephson junctions via phase control
• Topological superconductor with a large Chern number and a large bulk excitation gap in single layer graphene
• Topological spin-singlet superconductors with underlying sublattice structure
• Inducing chiral superconductivity on honeycomb lattice systems
• Edge states, spin transport and impurity induced local density of states in spin-orbit coupled graphene
• New spinor classes on the Graf-Clifford algebra
• Electron dynamics in graphene with spin-orbit couplings and periodic potentials
• Quantized Thermal Hall Conductance and the Topological Phase Diagram of a Superconducting Bismuth Bilayer
• Topological in-gap chiral edge states in superconducting Haldane model with spin-orbit coupling
• Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity
• Chiral Majorana Fermions in two dimensional square lattice antiferromagnet with proximity-induced superconductivity