Braiding Majorana Zero Modes in Spin Space: From Worldlines to Worldribbons
Prof. Xin Liu got his B.S. degree in Nankai University and M.S. degree in Chern Institute of Mathematics, Tianjin. He received his Ph. D. from Texas A&M University in 2012. After graduation, he had worked as a postdoctoral researcher in the Pennsylvania State University from 2012 to 2014 and Condensed Matter Theory Center, University of Maryland from 2014-2015. He joined Huazhong University of Science and Technology in 2015.
Confirming the existence of Majorana zero modes (MZMs) is one of the most essential problems in the current condensed matter field. The most convincing experimental program is to detect the non-Abelian braiding statistics through braiding MZMs, which is also the most crucial step towards topological quantum computation. In this talk, I will first give an intuitive introduction of topological superconductor, MZMs and associated non-Abelian braiding statistics. A brief review for the recent experimental progresses in detecting MZMs and theoretical proposals of braiding MZMs will be present. I then introduce our previous work about spin property of MZMs and show why and how spin can play an important role in Majorana physics. Following this idea, I will focus on our recent work, proposing a new scheme to braid MZMs without moving and measuring, or more extension fusing them. Our scheme is explicitly manifested in a two dimensional topological insulator, proximity coupled to superconductors and ferromagnetic insulators. We show that braiding two MZMs can be realized by manipulating the actual spin of MZMs. The accurate braiding operation is robust against the inaccuracy of manipulations and quasiparticle poisoning. As the proposed device contains only four MZMs, keeping well separated during the braiding process, and no ancillary MZMs are required, our scheme is immune to quantum information leakage.