Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model

TL;DR

This paper investigates how topological defects in Kitaev's honeycomb model host unpaired Majorana modes, revealing their robustness and the role of gauge fields in their physics.

Contribution

It demonstrates that certain dislocations and string defects in the model carry unpaired Majorana fermions, advancing understanding of topological excitations in spin liquids.

Findings

Dislocations and string defects host unpaired Majorana fermions.

Majorana modes are robust against local noise.

Gauge fields play a crucial role in Majorana mode physics.

Abstract

We study the gapped phase of Kitaev's honeycomb model (a $Z_2$ spin liquid) on a lattice with topological defects. We find that some dislocations and string 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 one of the dislocations. The exact solution respects gauge invariance and reveals a crucial role of the gauge field in the physics of Majorana modes. To facilitate these theoretical developments, we recast the degenerate perturbation theory for spins in the language of Majorana fermions.