Non-Abelian Braiding of Majorana zero modes in a topological Josephson Junction

We theoretically study a Josephson junction which is formed of finite size superconductors on a topological insulator under a magnetic field. An extended chiral Majorana mode emerges surrounding two superconductors, in addition to localized Majorana zero modes along the junction under a certain number of magnetic flux quanta piercing the junction. We find that the qubit state composed of the Majorana zero modes can be manipulated by a bias voltage across the superconductors. The non-Abelian braiding of Majorana zero modes can be detected by the Josephson current.