The Dirac semimetal phase found in ${\mathrm{Cd}}_3{\mathrm{As}}_2$ 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 ${\mathrm{Cd}}_3{\mathrm{As}}_2$ using a combined approach of scanning tunneling microscopy and ab initio calculations. We determine the exact position of the (112) plane at which ${\mathrm{Cd}}_3{\mathrm{As}}_2$ 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.

• Received 12 October 2016
• Revised 28 December 2016
• Corrected 7 April 2017
• Publisher error corrected 3 March 2017

DOI:https://doi.org/10.1103/PhysRevB.95.081410