  The Dirac point gap at the surface of the antiferromagnetic topological
insulator MnBi$_2$Te$_4$ is a highly debated issue. While the early
photoemission measurements reported on large gaps in agreement with theoretical
predictions, other experiments found vanishingly small splitting of the
MnBi$_2$Te$_4$ Dirac cone. Here, we study the crystalline and electronic
structure of MnBi$_2$Te$_4$(0001) using scanning tunneling
microscopy/spectroscopy (STM/S), micro($\mu$)-laser angle resolved
photoemission spectroscopy (ARPES), and density functional theory (DFT)
calculations. Our topographic STM images clearly reveal features corresponding
to point defects in the surface Te and subsurface Bi layers that we identify
with the aid of STM simulations as Bi$_\text{Te}$ antisites (Bi atoms at the Te
sites) and Mn$_\text{Bi}$ substitutions (Mn atoms at the Bi sites),
respectively. X-ray diffraction (XRD) experiments further evidence the presence
of cation (Mn-Bi) intermixing. Altogether, this affects the distribution of the
Mn atoms, which, inevitably, leads to a deviation of the MnBi$_2$Te$_4$
magnetic structure from that predicted for the ideal crystal structure. Our
transport measurements suggest that the degree of this deviation varies from
sample to sample. Consistently, the ARPES/STS experiments reveal that the Dirac
point gap of the topological surface state is different for different
samples/sample cleavages. Our DFT surface electronic structure calculations
show that, due to the predominant localization of the topological surface state
near the Bi layers, Mn$_\text{Bi}$ defects can cause a strong reduction of the
MnBi$_2$Te$_4$ Dirac point gap, given the recently proved antiparallel
alignment of the Mn$_\text{Bi}$ moments with respect to those of the Mn layer.
Our results provide a key to puzzle out the MnBi$_2$Te$_4$ Dirac point gap
mystery.
