Unpaired Majorana modes in the gapped phase of Kitaev's honeycomb model

Abstract

We study the gapped phase of Kitaev's honeycomb model (a Z_2 spin liquid) in the presence of lattice defects. We find that some dislocations and bond defects carry unpaired Majorana fermions. Physical excitations associated with these defects are (complex) fermion modes made out of two (real) Majorana fermions connected by a Z_2 gauge string. The quantum state of these modes is robust against local noise and can be changed by winding a Z_2 vortex around a dislocation. The exact solution respects gauge invariance and reveals a crucial role of the gauge field in the physics of Majorana modes.

References in corpus (6)

• Topological Defects in Graphene: Dislocations and Grain Boundaries
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Genons, twist defects, and projective non-Abelian braiding statistics
• Effects of topological defects and local curvature on the electronic properties of planar graphene
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• Dislocations in graphene

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