  The Weyl semimetal requires the breaking of either the time-reversal symmetry
(TRS) or the lattice inversion symmetry. When the TRS and inversion symmetry
coexist, a pair of degenerate Weyl points may exist, leading to the related
Dirac semimetal phase. In other words, a Dirac semimetallic state can be
regarded as two copies of Weyl semimetal states. In this dissertation, we study
tellurium based compounds like the Weyl semimetal candidate MoTe2 and the Dirac
semimetal candidate PtTe2 within the transition metal dichalcogenides family.
