Identifying true Majorana zero modes through their non-Abelian statistics

Establishing a superconducting topological phase is the first step in realizing Majorana-based topological quantum computation, which relies on the braiding and fusion of Majorana zero modes. In this work, we numerically investigate the parameter space of the Kitaev model and find regions where the hybridization energy between the Majorana modes, detrimental, e.g., to qubit operations, is zero even in the presence of moderate disorder. We show that the operator γ², associated with this low-energy mode, as a function of the parameters of the system presents a plateau pinned to 1 as opposed to ordinary fermions that have γ² = 0. We use the operator γ to identify true Majorana zero-energy states with non-Abelian statistics. In addition, we propose a way of probing these zero-energy solutions by coupling a quantum dot to the Kitaev wire [1]. The Majorana signature emerges as a e²/2h peak in the conductance of the dot when the dot level is far detuned from the Fermi energy. Our findings show an optimal parameter regime of finite Majorana wires to suppress the hybridization energy, which might guide the choice of parameters in future experiments.

[1] E. Vernek, P. H. Penteado, A. C. Seridonio, and J. C. Egues, Subtle leakage of a Majorana mode into a quantum dot. Phys. Rev. B 89, 165314 (2014)