  Dirac semimetal (DSM) hosts four-fold degenerate isolated band-crossing
points with linear dispersion, around which the quasiparticles resemble the
relativistic Dirac Fermions. It can be described by a 4 * 4 massless Dirac
Hamiltonian which can be decomposed into a pair of Weyl points or gaped into an
insulator. Thus, crystal symmetry is critical to guarantee the stable
existence. On the contrary, by breaking crystal symmetry, a DSM may transform
into a Weyl semimetal (WSM) or a topological insulator (TI). Here, by taking
hexagonal LiAuSe as an example, we find that it is a starfruit shaped multiple
nodal chain semimetal in the absence of spin-orbit coupling(SOC). In the
presence of SOC, it is an ideal DSM naturally with the Dirac points locating at
Fermi level exactly, and it would transform into WSM phase by introducing
external Zeeman field or by magnetic doping with rare-earth atom Sm. It could
also transform into TI state by breaking rotational symmetry. Our studies show
that DSM is a critical point for topological phase transition, and the
conclusion can apply to most of the DSM materials, not limited to the hexagonal
material LiAuSe.
