We investigate topological features of electronic structures which produce large anomalous Hall effect in the non-collinear antiferromagnetic metallic states of anti-perovskite manganese nitrides by first-principles calculations. We first predict the stable magnetic structures of these compounds to be non-collinear antiferromagnetic structures characterized by either T1g or T2g irreducible representation by evaluating the total energy for all of the magnetic structures classified according to the symmetry and multipole moments. The topology analysis is next performed for the Wannier tight-binding models obtained from the first-principles band structures. Our results reveal the small Berry curvature induced through the coupling between occupied and unoccupied states with the spin-orbit coupling, which is widely spread around the Fermi surface in the Brillouin zone, dominantly contributes after the k-space integration to the anomalous Hall conductivity, while the local divergent Berry curvature around Weyl points has a rather small contribution to the anomalous Hall conductivity.
This work is devoted for gauge boson sector of the recently proposed model based on SU(3) C ⊗ SU(3) L ⊗ U(1) X group with minimal content of leptons and Higgses. The limits on the masses of the bilepton gauge bosons and on the mixing angle among the neutral ones are deduced. Using the Fritzsch anzats on quark mixing, we show that the third family of quarks should be different from the first two. We obtain a lower bound on mass of the new heavy neutral gauge boson as 6.051 TeV. Using data on branching decay rates of the Z boson, we can fix the limit to the Z and Z ′ mixing angle φ as −0.001 ≤ φ ≤ 0.0003.
The mixing among gauge bosons in the 3-3-1 models with the discrete symmetries is investigated. To get tribimaximal neutrino mixing, we have to introduce sextets containing neutral scalar components with lepton numberL=1,2. Assignation of VEVs to these fields leads to the mixing of the new gauge bosons and those in the standard model. The mixing in the charged gauge bosons leads to the lepton number violating interactions of theWboson. The same situation happens in the neutral gauge boson sector.
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