  Defect centers in insulators play a critical role in creating important
functionalities in materials: prototype qubits, single-photon sources, magnetic
field probes, and pressure sensors. These functionalities are highly dependent
on their mid-gap electronic structure and orbital/spin wave-function
contributions. However, in most cases, these fundamental properties remain
unknown or speculative due to the defects being deeply embedded beneath the
surface of highly resistive host crystals, thus impeding access through surface
probes. Here, we directly inspected the atomic and electronic structures of
defects in thin carbon-doped hexagonal boron nitride (hBN:C) using scanning
tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Such
investigation adds direct information about the electronic mid-gap states to
the well-established photoluminescence response (including single photon
emission) of intentionally created carbon defects in the most commonly
investigated van der Waals insulator. Our joint atomic-scale experimental and
theoretical investigations reveal two main categories of defects: 1)
single-site defects manifesting as donor-like states with atomically resolved
structures observable via STM, and 2) multi-site defect complexes exhibiting a
ladder of empty and occupied mid-gap states characterized by distinct spatial
geometries. Combining direct probing of mid-gap states through tunneling
spectroscopy with the inspection of the optical response of insulators hosting
specific defect structures holds promise for creating and enhancing
functionalities realized with individual defects in the quantum limit. These
findings underscore not only the versatility of hBN:C as a platform for quantum
defect engineering but also its potential to drive advancements in atomic-scale
optoelectronics.
