  Spatially resolved EELS has been performed at diffuse interfaces between
MoS$_2$ and MoSe$_2$ single layers. With a monochromated electron source (20
meV) we have successfully probed excitons near the interface by obtaining the
low loss spectra at the nanometer scale. The exciton maps clearly show
variations even with a 10 nm separation between measurements; consequently the
optical bandgap can be measured with nanometer-scale resolution, which is 50
times smaller than the wavelength of the emitted photons. By performing
core-loss EELS at the same regions, we observe that variations in the excitonic
signature follow the chemical composition. The exciton peaks are observed to be
broader at interfaces and heterogeneous regions, possibly due to interface
roughness and alloying effects. Moreover, we do not observe shifts of the
exciton peak across the interface, possibly because the interface width is not
much larger than the exciton Bohr radius.
