Phys. Rev. B 101, 205401 (2020)

Nonlocality of Majorana zero modes and teleportation: Self-consistent treatment based on the Bogoliubov–de Gennes equation

Xin-Qi Li* and Luting Xu

Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300072, China

* xinqi.li@tju.edu.cn

ABSTRACT

The nonlocal nature of the Majorana zero modes implies an inherent teleportation channel and unique transport signatures for Majorana identification. In this work we make an effort to eliminate some inconsistencies between the Bogoliubov–de Gennes equation based treatment and the method using the associated regular fermion-number states of occupation within the “second quantization” framework. We first consider a rather simple “quantum dot–Majorana wire–quantum dot” system, then a more experimentally relevant setup by replacing the quantum dots with transport leads. For the latter setup, based on the dynamical evolution of electron-hole excitations, we develop a single-particle wave-function approach to quantum transport, which renders both the conventional quantum scattering theory and the steady-state nonequilibrium Green's function formalism as its stationary limit. Further, we revisit the issue of Majorana tunneling spectroscopy and consider in particular the two-lead coupling setup. We present comprehensive discussions with detailed comparisons, and predict a zero-bias-limit conductance of e²/h (for symmetric coupling to the leads), which is a half of the popular result of the zero-bias peak or the so-called Majorana quantized conductance (2e²/h). This work may arouse a need to reexamine some existing studies and the proposed treatment is expected to be involved in analyzing future experiments in this fast developing field.