Atomically Resolved STM Characterization of the 3-D Dirac Semimetal Cd$_{3}$As$_{2}$

Dirac semimetals such as Cd$_{3}$As$_{2}$ are a recently discovered class of materials which host three-dimensional linear dispersion around point-like band crossings in the bulk Brillouin zone, and hence represent three-dimensional analogues of graphene. This electronic phase is enabled by specific crystal symmetries: In the case of Cd$_{3}$As$_{2}$, a C$_{4}$ rotational symmetry associated with its peculiar corkscrew arrangement of systematic Cd vacancies. Although this arrangement underpins the current crystallographic understanding of Cd$_{3}$As$_{2}$, and all its theoretical implications, it is strangely absent in surface microscopic investigations reported previously. Here we use a combined approach of scanning tunneling microscopy and ab initio calculations to show that the currently held crystallographic model of Cd$_{3}$As$_{2}$ is indeed predictive of a periodic zig-zag superstructure at the (112) surface, which we observe in scanning tunneling microscopy images. This helps to reconcile the current state of microscopic surface observations with the prevailing crystallographic and theoretical models.