Non-Abelian Majorana Doublets in Time-Reversal Invariant Topological Superconductor

TL;DR

This paper demonstrates that non-Abelian Majorana doublets in time-reversal invariant topological superconductors can exhibit non-Abelian statistics and influence Josephson effects, advancing potential quantum computing applications.

Contribution

It reveals non-Abelian statistics in 1D TRI topological superconductors and links Josephson current periodicity to fermion parity, offering new quantum measurement methods.

Findings

Non-Abelian Majorana doublets can exist in 1D TRI superconductors.

Josephson current periodicity depends on fermion parity.

Potential applications in topological quantum computation.

Abstract

The study of non-Abelian Majorana zero modes advances our understanding of the fundamental physics in quantum matter, and pushes the potential applications of such exotic states to topological quantum computation. It has been shown that in two-dimensional (2D) and 1D chiral superconductors, the isolated Majorana fermions obey non-Abelian statistics. However, Majorana modes in a $Z_2$ time-reversal invariant (TRI) topological superconductor come in pairs due to Kramers' theorem. Therefore, braiding operations in TRI superconductors always exchange two pairs of Majoranas. In this work, we show interestingly that, due to the protection of time-reversal symmetry, non-Abelian statistics can be obtained in 1D TRI topological superconductors and may have advantages in applying to topological quantum computation. Furthermore, we unveil an intriguing phenomenon in the Josephson effect, that the periodicity of Josephson currents depends on the fermion parity of the superconducting state. This effect provides direct measurements of the topological qubit states in such 1D TRI superconductors.