Coupled Majorana modes in a dual vortex of the Kitaev honeycomb model
Abstract
The Kitaev model is exactly solvable in terms of Majorana fermions hopping on a honeycomb lattice and coupled to a static Z 2 gauge field, giving the possibility of π vortices in hexagonal plaquettes. In the vortex-full sector and in the presence of a time-reversal-breaking three-spin term of strength κ, the energy spectrum is gapped, and the ground state possesses an even Chern number. An isolated vortex-free plaquette acts as a dual vortex and binds a fermionic mode at finite energy in the bulk gap. This mode is equivalent to two coupled Majorana zero modes located on the same dual vortex. In a continuum approximation, we analytically compute the Majorana wave functions and their coupling in the two limits of small or large κ. The analytical approach is confirmed by numerical perturbation theory directly on the lattice. The latter is in excellent agreement with the full numerics on a finite-size system. We contrast our results with states bound to an isolated vortex in a topological superconductor with even Chern number.
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BibTeX
@article{basak2026coupled,
title = {{Coupled Majorana modes in a dual vortex of the Kitaev honeycomb model}},
author = {Surajit Basak and Jean-Noël Fuchs},
journal = {Physical Review B},
year = {2026},
month = aug,
doi = {10.1103/qhsx-q63d},
url = {https://hal.science/hal-05765719v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Coupled Majorana modes in a dual vortex of the Kitaev honeycomb model
AU - Surajit Basak
AU - Jean-Noël Fuchs
PY - 2026
DA - 2026/08/31
JO - Physical Review B
DO - 10.1103/qhsx-q63d
UR - https://hal.science/hal-05765719v1
AB - The Kitaev model is exactly solvable in terms of Majorana fermions hopping on a honeycomb lattice and coupled to a static Z 2 gauge field, giving the possibility of π vortices in hexagonal plaquettes. In the vortex-full sector and in the presence of a time-reversal-breaking three-spin term of strength κ, the energy spectrum is gapped, and the ground state possesses an even Chern number. An isolated vortex-free plaquette acts as a dual vortex and binds a fermionic mode at finite energy in the bulk gap. This mode is equivalent to two coupled Majorana zero modes located on the same dual vortex. In a continuum approximation, we analytically compute the Majorana wave functions and their coupling in the two limits of small or large κ. The analytical approach is confirmed by numerical perturbation theory directly on the lattice. The latter is in excellent agreement with the full numerics on a finite-size system. We contrast our results with states bound to an isolated vortex in a topological superconductor with even Chern number.
SN - 2469-9950
SN - 2469-9969
ER -