Defects in Graphene : A Topological Description

Abstract

Specific types of spatial defects or potentials can turn monolayer graphene into a topological material. These topological defects are classified by a spatial dimension $D$ and they are systematically obtained from the Hamiltonian by means of its symbol $\mathcal{H}(\mathbf{k},\mathbf{r})$, an operator which generalises the Bloch Hamiltonian and contains all topological information. This approach, when applied to Dirac operators, allows to recover the tenfold classification of insulators and superconductors. The existence of a stable $\mathbb{Z}$-topology is predicted as a condition on the dimension $D$, similar to the classification of defects in thermodynamic phase transitions. Kekule distortions, vacancies and adatoms in graphene are proposed as examples of such defects and their topological equivalence is discussed.

11 pages

References in corpus (11)

• The electronic properties of graphene
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Cited by in corpus (3)

• Observation of Kekulé vortices induced in graphene by hydrogen adatoms
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Topological Tenfold Classification and the Entanglement of Two Qubits