Realization and Noise Effect of Majorana Fermions in Topological Superconductors

Abstract

In the thesis, Chapter 1 is an introduction to topological superconductors, from which one can have some basic understanding on Majorana fermions. In Chapter 2, we study the noise effect in time invariant topological superconductor. In presence of time dependent noise, local mixing among Majorana Kramer’s pair will happen. However, we show that noise effect could be highly suppressed, as (i) transition among Majorana Kramer’s pair is a second order transition (ii) transition among Majorna Kramer’s pair only happens when the correlation function of noise potential breaks the time reversal symmetry (iii) small spatial correlation length of noise potential will decrease the strength of coupling between Majoranas and bath states. Finally, we also suggest that non-Abelian operation among DIII-class Majoranas-based qubits, with a continuum of angles, could be achieved by using local time dependent operation on Majorana Kramer’s pair. In Chapter 3, we show how to realize Majroana flat band with a ferromagnetic multilayers on the top of s$\pm$-wave SCs. In Chapter 4, we showed some numerical results about the non-Abelian states on the Möbius stripe.