Spatial Charge Inhomogeneity and Defect States in Topological Dirac Semimetal Thin Films

Dirac materials are characterized by a charge neutrality point, where the system breaks into electron/hole puddles. In graphene, substrate disorder drives fluctuations in $E_{F}$, necessitating ultra-clean substrates to observe Dirac point physics. Three-dimensional topological Dirac semimetals (TDS) obviate the substrate, and should show reduced $E_{F}$ fluctuations due to better metallic screening and higher dielectric constants. Yet, the local response of the charge carriers in a TDS to various perturbations has yet to be explored. Here we map the potential fluctuations in TDS 20nm Na$_{3}$Bi films grown via MBE using scanning tunneling microscopy/spectroscopy. The potential fluctuations are significantly smaller than room temperature ($\Delta E_{F\, }\approx $ 5 meV $=$ 60 K) and comparable to the highest quality graphene on h-BN; far smaller than graphene on SiO$_{2}$,$^{\, }$or the Dirac surface state of a topological insulator. This observation bodes well for exploration of Dirac point physics in TDS materials. Furthermore, surface Na vacancies show a bound resonance state close to the Dirac point with large spatial extent, a possible analogue to resonant impurities in graphene.