Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice

Abstract

We investigate a number of fermionic condensate phases on the honeycomb lattice, to determine whether topological defects (vortices and edges) in these phases can support bound states with zero energy. We argue that topological zero modes bound to vortices and at edges are not only connected, but should in fact be \emph{identified}. Recently, it has been shown that the simplest s-wave superconducting state for the Dirac fermion approximation of the honeycomb lattice at precisely half filling, supports zero modes inside the cores of vortices (P. Ghaemi and F. Wilczek, 2007). We find that within the continuum Dirac theory the zero modes are not unique neither to this phase, nor to half filling. In addition, we find the \emph{exact} wavefunctions for vortex bound zero modes, as well as the complete edge state spectrum of the phases we discuss. The zero modes in all the phases we examine have even-numbered degeneracy, and as such pairs of any Majorana modes are simply equivalent to one ordinary fermion. As a result, contrary to bound state zero modes in $p_x+i{p}_y$ superconductors, vortices here do \emph{not} exhibit non-Abelian exchange statistics. The zero modes in the pure Dirac theory are seemingly topologically protected by the effective low energy symmetry of the theory, yet on the original honeycomb lattice model these zero modes are split, by explicit breaking of the effective low energy symmetry.

Final version including numerics, accepted for publication in PRB

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• Chain of Majorana States from Superconducting Dirac Fermions at a Magnetic Domain Wall
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• Majorana zero modes bound to a vortex line in a topological superconductor
• Competing Superconducting States for Ultracold Atoms in Optical Lattices with Artificial Staggered Magnetic Field
• Pairing symmetry and vortex zero-mode for superconducting Dirac fermions
• Z${}_2$ index theorem for Majorana zero modes in a class D topological superconductor
• Supersymmetric Runge-Lenz-Pauli vector for Dirac vortex in topological insulators and graphene
• Realization of a vortex in the Kekule texture of molecular Graphene, at a Y junction where 3 domains meet
• Gapless vortex bound states in superconducting topological semimetals
• Current Density of Majorana Bound States
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• Local breaking of the spin degeneracy in the vortex states of Ising superconductors: Induced antiphase ferromagnetic order