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Dirac semimetal (DSM) hosts four-fold degenerate isolated band-crossingpoints with linear dispersion, around which the quasiparticles resemble therelativistic Dirac Fermions. It can be described by a 4 * 4 massless DiracHamiltonian which can be decomposed into a pair of Weyl points or gaped into aninsulator. Thus, crystal symmetry is critical to guarantee the stableexistence. On the contrary, by breaking crystal symmetry, a DSM may transforminto a Weyl semimetal (WSM) or a topological insulator (TI). Here, by takinghexagonal LiAuSe as an example, we find that it is a starfruit shaped multiplenodal chain semimetal in the absence of spin-orbit coupling(SOC). In thepresence of SOC, it is an ideal DSM naturally with the Dirac points locating atFermi level exactly, and it would transform into WSM phase by introducingexternal Zeeman field or by magnetic doping with rare-earth atom Sm. It couldalso transform into TI state by breaking rotational symmetry. Our studies showthat DSM is a critical point for topological phase transition, and theconclusion can apply to most of the DSM materials, not limited to the hexagonalmaterial LiAuSe.

From Multiple Nodal Chain to Dirac/Weyl Semimetal and Topological Insulator in Ternary Hexagonal Materials