Topological qubits in graphenelike systems

Abstract

The fermion-doubling problem can be an obstacle to getting half-a-qubit in two-dimensional fermionic tight-binding models in the form of Majorana zero modes bound to the core of superconducting vortices. We argue that the number of such Majorana zero modes is determined by a Z_2 x Z_2 topological charge for a family of two-dimensional fermionic tight-binding models ranging from noncentrosymmetric materials to graphene. This charge depends on the dimension of the representation (i.e., the number of species of Dirac fermions -- where the doubling problem enters) and the parity of the Chern number induced by breaking time-reversal symmetry. We show that in graphene there are as many as ten order parameters that can be used in groups of four to change the topological number from even to odd.

5 pages; 2 figures; 1 table

References in corpus (7)

• The electronic properties of graphene
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• A generic new platform for topological quantum computation using semiconductor heterostructures
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Conformal invariance of chiral edge theories
• Superconductivity on the surface of topological insulators and in two-dimensional noncentrosymmetric materials

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• Anderson localization and the topology of classifying spaces
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• Topological superconductors as nonrelativistic limits of Jackiw-Rossi and Jackiw-Rebbi models
• Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
• Magnetic field induced inequivalent vortex zero modes in strained graphene
• Masses and Majorana fermions in graphene
• $Z_2$ index for gapless fermionic modes in the vortex core of three dimensional paired Dirac fermions
• Competing orders in the Dirac-like electronic structure and the non-linear sigma model with the topological terms
• An effective model for the electronic and optical properties of stanene
• Spin and angular resolved photoemission experiments on epitaxial graphene
• Half vortex and fractional electrical charge in two dimensions