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

TL;DR

This paper investigates the gapped phase of Kitaev's honeycomb model with lattice defects, revealing that certain defects host unpaired Majorana fermions, which are robust and can be manipulated via Z_2 vortices, highlighting the role of gauge fields.

Contribution

It demonstrates the existence of unpaired Majorana modes at lattice defects in the gapped phase of Kitaev's honeycomb model, emphasizing the gauge field's role in their physics.

Findings

Certain dislocations host unpaired Majorana fermions.

Majorana modes are robust against local noise.

Winding Z_2 vortices can change the quantum state of these modes.

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.