Coexistence of spin-1 fermion and Dirac fermion on the triangular kagome lattice

Quasiparticle excitations beyond the Dirac-Weyl-Majorana classification can appear in lattice systems due to a lesser symmetry constraint compared with Poincar\'e symmetry in high-energy physics. In particular, fermions with an integer spin can appear in a variety of lattices. Here, we show that two-dimensional spin-1 fermions may coexist with Dirac fermions in the triangular kagome lattice (TKL). We derive a four-band effective model that hosts both types of fermions. The effective model can be used to study the interplay between spin-1 and spin-1/2 fermions. As an example, using this model we show that spin-nonconserving Klein tunneling can occur in the TKL, which has a transmission coefficient $T=1$ for normal incidence. Our findings pave a way to the study of the interaction and interplay between different types of fermions in lattice systems.