Recent progress on non-Abelian anyons: from Majorana zero modes to topological Dirac fermionic modes

Abstract

Majorana zero modes (MZMs) have been intensively studied in recent decades theoretically and experimentally as the most promising candidate for non-Abelian anyons supporting topological quantum computation (TQC). In addition to the Majorana scheme, some non-Majorana quasiparticles obeying non-Abelian statistics, including topological Dirac fermionic modes, have also been proposed and therefore become new candidates for TQC. In this review, we overview the non-Abelian braiding properties as well as the corresponding braiding schemes for both the MZMs and the topological Dirac fermionic modes, emphasizing the recent progress on topological Dirac fermionic modes. A topological Dirac fermionic mode can be regarded as a pair of MZMs related by unitary symmetry, which can be realized in a number of platforms, including the one-dimensional topological insulator, higher-order topological insulator, and spin superconductor. This topological Dirac fermionic mode possesses several advantages compared with its Majorana cousin, such as superconductivity-free and larger gaps. Therefore, it provides a new avenue for investigating non-Abelian physics and possible TQC.