  A topological Dirac semimetal is a novel state of quantum matter which has
recently attracted much attention as an apparent 3D version of graphene. In
this paper, we report critically important results on the electronic structure
of the 3D Dirac semimetal Na3Bi at a surface that reveals its nontrivial
groundstate. Our studies, for the first time, reveal that the two 3D Dirac
cones go through a topological change in the constant energy contour as a
function of the binding energy, featuring a Lifshitz point, which is missing in
a strict 3D analog of graphene (in other words Na3Bi is not a true 3D analog of
graphene). Our results identify the first example of a band saddle point
singularity in 3D Dirac materials. This is in contrast to its 2D analogs such
as graphene and the helical Dirac surface states of a topological insulator.
The observation of multiple Dirac nodes in Na3Bi connecting via a Lifshitz
point along its crystalline rotational axis away from the Kramers point serves
as a decisive signature for the symmetry-protected nature of the Dirac
semimetal's topological groundstate.
