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

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 scheme, some non-Majorana quasiparticles obeying statistics, including Dirac fermionic modes, also proposed therefore become new candidates TQC. this review, we overview braiding properties well corresponding schemes both MZMs emphasizing progress on modes. A mode can be regarded a pair of related by unitary symmetry, which realized number platforms, one-dimensional insulator, higher-order spin superconductor. This possesses several advantages compared with its cousin, such superconductivity-free larger gaps. Therefore, it provides avenue investigating physics possible