Realizing Majorana fermion modes in the Kitaev model

TL;DR

This paper demonstrates that applying a uniform magnetic field to the Kitaev model can produce robust Majorana zero modes bound to defects, which are promising for topological quantum computing.

Contribution

It shows how to realize and manipulate Majorana zero modes in the Kitaev model using a magnetic field and defects, advancing topological quantum computing.

Findings

Majorana zero modes are bound to defects in the Kitaev model.

These modes decay exponentially and are robust against local perturbations.

The system can be turned into an effective p+ip superconductor with a magnetic field.

Abstract

We study the possibility to realize Majorana zero mode that's robust and may be easily manipulated for braiding in quantum computing in the ground state of the Kitaev model in this work. To achieve this we first apply a uniform [111] magnetic field to the gapless Kitaev model and turn the Kitaev model to an effective p + ip topological superconductor of spinons. We then study possible vortex binding in such system to a topologically trivial spot in the ground state. We consider two cases in the system: one is a vacancy and the other is a fully polarized spin. We show that in both cases, the system binds a vortex with the defect and a robust Majorana zero mode in the ground state at a weak uniform [111] magnetic field. The distribution and asymptotic behavior of these Majorana zero modes is studied. The Majorana zero modes in both cases decay exponentially in space, and are robust against local perturbations and other Majorana zero modes far away, which makes them promising candidate for braiding in topological quantum computing.