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

We study the gapped phase of Kitaev's honeycomb model (a Z₂ 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 Z₂ gauge string. The quantum state of these modes is robust against local noise and can be changed by winding a Z₂ 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.