  The exceptional electronic, optical and chemical properties of
two-dimensional materials strongly depend on the 3D atomic structure and
crystal defects. Using Re-doped MoS2 as a model, here we develop scanning
atomic electron tomography (sAET) to determine the 3D atomic positions and
crystal defects such as dopants, vacancies and ripples with a precision down to
4 picometers. We measure the 3D bond distortion and local strain tensor induced
by single dopants for the first time. By directly providing experimental 3D
atomic coordinates to density functional theory (DFT), we obtain more truthful
electronic band structures than those derived from conventional DFT
calculations relying on relaxed 3D atomic models, which is confirmed by
photoluminescence measurements. We anticipate that sAET is not only generally
applicable to the determination of the 3D atomic coordinates of 2D materials,
heterostructures and thin films, but also could transform ab initio
calculations by using experimental 3D atomic coordinates as direct input to
better predict and discover new physical, chemical and electronic properties.
