Non-Abelian Charge Transport in Three-Flavor Gauge Semimetal Model with Braiding Majoranas

Known Majorana fermions models are considered as promising ones for the purposes of quantum computing robust to decoherence. One of the most expecting but unachieved goals is an effective control for braiding of Majoranas. Another one is to describe ${\mathbb{Z}}_2$ topological semimetals, APRES spectra of which testify on eight-fold degenerate chiral fermions with $SU(2)$ holonomy of wave functions, whereas the last can not be reproduced within existing models. Quasi-relativistic theory of non-abelian quantum charge transport in topological semimetals is developed for a model with a number of flavors equal three. Majorana-like quasi-particle excitations in the model are described with accounting of dynamic mass term arising due to relativistic exchange interactions. Such exotic features of $\mathbb{Z}_2$ semimetals as splitting zero-conductance peaks, longitudinal magnetoresistance, minimal direct current conductivity, negative differential conductivity have been calculated in perfect agreement with experimental data. We propose a new scheme of braiding for three flavor Majorana-like fermions with new non-trivial braiding operator. We demonstrate that in this model, the presence of chiral Majorana-like bound states is controlled as emergence of three pairs of resonance-antiresonance in frequency dependence of dielectric permeability.