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

Quasiparticle excitations beyond Dirac-Weyl-Majorana classification can appear in lattice systems due to the less 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 fermion 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 the 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.