title: New scheme for braiding Majorana fermions.
abstract: Non-Abelian statistics can be achieved by exchanging two vortices in topological superconductors with each grabbing a Majorana fermion (MF) as zero-energy quasi-particle at the cores. However, in experiments it is difficult to manipulate vortices. In the present work, we propose a way to braid MFs without moving vortices. The only operation required in the present scheme is to turn on and off local gate voltages, which liberates a MF from its original host vortex and transports it along the prepared track. We solve the time-dependent Bogoliubov-de Gennes equation numerically, and confirm that the MFs are protected provided the switching of gate voltages for exchanging MFs are adiabatic, which takes only several nano seconds given reasonable material parameters. By monitoring the time evolution of MF wave-functions, we show that non-Abelian statistics is achieved.
authors.affiliation: International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science, Tsukuba 305-0044, Japan; Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571, Japan.
authors.forename: Long-Hua
authors.initials: LH
authors.lastname: Wu
authors.affiliation: International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science, Tsukuba 305-0044, Japan; Department of Physics, Shaoxing University, Shaoxing 312000, People's Republic of China.
authors.forename: Qi-Feng
authors.initials: QF
authors.lastname: Liang
authors.affiliation: International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science, Tsukuba 305-0044, Japan; Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571, Japan.
authors.forename: Xiao
authors.initials: X
authors.lastname: Hu
keywords: Bogoliubov–de Gennes equation; Majorana fermion; non-Abelian statistics; quantum computation; topological superconductor