  Recent researches show that by breaking inversion symmetry Dirac fermions can
split into new fermions with 3-component. In this article, we demonstrate that
Dirac fermions can also split into 3-component fermions with time reversal
symmetry (TRS) breaking while inversion symmetry is preserved. Firstly, we
conduct a symmetry analysis with the commutation relations among all symmetry
operators of a Dirac semimetal and find out the symmetry conditions of Dirac
fermions splitting into 3-component fermions. With the symmetry conditions, we
derive the $k\cdot P$ effective Hamiltonian of TRS breaking and compare it with
the Hamiltonian of inversion symmetry breaking. We find that they are different
in $\Gamma$ point eigenenergies. This can be considered as consequence of
Kramers degeneracy breaking which is a clear signature of TRS breaking.
Moreover, with the $k\cdot P$ effective Hamiltonian of the system we show that
TRS-breaking-induced 3-component fermions can split into Weyl fermions while a
small magnetic field is applied. At the end, we show our first principles
calculation results are consistent with the symmetry analysis and the $k\cdot
P$ predictions. Our work clarifies the similarities and the differences between
TRS-breaking-induced 3-component fermions and
inversion-symmetry-breaking-induced 3-component fermions and extends the scope
of 3-component fermion behaviors.
