Lifshitz transition and Van Hove singularity in a three-dimensional topological Dirac semimetal

A three-dimensional (3D) 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 results on the electronic structure of the 3D Dirac semimetal ${\mathrm{Na}}_3\mathrm{Bi}$ at a surface that reveals its nontrivial ground state. Our studies 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. Our results identify an example of a band saddle-point singularity in 3D Dirac materials. This is in contrast to its two-dimensional analogs such as graphene and the Dirac surface states of a topological insulator. The observation of multiple Dirac nodes in ${\mathrm{Na}}_3\mathrm{Bi}$ 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 bulk ground state.