Masses and Majorana fermions in graphene

Abstract

We review the classification of all the 36 possible gap-opening instabilities in graphene, i.e., the 36 relativistic masses of the two-dimensional Dirac Hamiltonian when the spin, valley, and superconducting channels are included. We then show that in graphene it is possible to realize an odd number of Majorana fermions attached to vortices in superconducting order parameters if a proper hierarchy of mass scales is in place.

Contribution to the Proceedings of the Nobel symposium on graphene and quantum matter

References in corpus (7)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Quantum Spin Hall Effect in Graphene
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Electron fractionalization in two-dimensional graphenelike structures
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Topological qubits in graphenelike systems

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• Engineering the Quantum Anomalous Hall Effect in Graphene with Uniaxial Strains
• Low energy electron-phonon effective action from symmetry analysis
• Spin Versus Charge Density Wave Order in Graphene-like Systems
• Topological spin-singlet superconductors with underlying sublattice structure
• Hall viscosity and nonlocal conductivity of "gapped graphene"
• To gap or not to gap? Mass distortions and edge modes in graphene armchair nanoribbons
• An effective model for the electronic and optical properties of stanene
• Fermion zero modes in a $Z_2$ vortex background
• Classification of mass terms in kagome semimetals