# Observation of surface superstructure induced by systematic vacancies in the topological Dirac semimetal Cd$_{3}$As$_{2}$

## TL;DR

This study combines microscopy and calculations to reveal a surface superstructure in Cd$_{3}$As$_{2}$ caused by systematic vacancies, crucial for its Dirac semimetal phase, and shows this structure persists after surface cleavage.

## Contribution

It provides the first microscopic observation and detailed structural analysis of vacancy-induced superstructure in Cd$_{3}$As$_{2}$, confirming its surface order and relevance to the Dirac phase.

## Key findings

- Identified the exact cleavage plane of Cd$_{3}$As$_{2}$.
- Observed a surface superstructure consistent with systematic vacancies.
- Confirmed the vacancy superstructure survives surface cleavage.

## Abstract

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 \textit{ab 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.