Observation of surface superstructure induced by systematic vacancies in the topological Dirac semimetal Cd${}_3$As${}_2$

The Dirac semimetal phase found in Cd${}_3$As${}_2$ is protected by a $C_4$ rotational symmetry derived from a corkscrew arrangement of systematic Cd vacancies in its complicated crystal structure. It is therefore surprising that no microscopic observation, direct or indirect, of these systematic vacancies has so far been described. To this end, we revisit the cleaved (112) surface of Cd${}_3$As${}_2$ using a combined approach of scanning tunneling microscopy and $\mathit{\text{ab}}\mathit{\text{initio}}$ calculations. We determine the exact position of the (112) plane at which Cd${}_3$As${}_2$ naturally cleaves, and describe in detail a structural periodicity found at the reconstructed surface, consistent with that expected to arise from the systematic Cd vacancies. This reconciles the current state of microscopic surface observations with those of crystallographic and theoretical models, and demonstrates that this vacancy superstructure, central to the preservation of the Dirac semimetal phase, survives the cleavage process and retains order at the surface.