Photoemission studies on the 3D Dirac semiemtal state in Na$_3$Bi*

A three-dimensional Dirac semimetal is a novel state of matter that has recently attracted interest in condensed matter physics and materials science. We present electronic structure measurements on the (100) surface of a recently discovered Dirac semimetal material Na$_3$Bi. Our experimental data, for the first time, reveal a Lifshitz transition between the two bulk Dirac cones in the bulk band structure of Na$_3$Bi. These results identify the first example of a band structure singularity in 3D Dirac materials. This is in contrast to its 2D analogs such as in twisted bilayer graphene or the surface states of topological crystalline insulators, which have been studied extensively. The observation of multiple bulk Dirac nodes along the rotational crystal axis away from the Kramers point also serve as a signature for the symmetry-protected nature of the Dirac semimetal state in Na$_3$Bi as elaborated in recent theories.