  Van der Waals (vdW) materials exhibit intriguing structural, electronic and
photonic properties. Electron Energy Loss Spectroscopy (EELS) within Scanning
Transmission Electron Microscope (STEM) allows for nanoscale mapping of such
properties. However, typical STEM-EELS detection is limited to energy losses in
the eV range, which are too large for probing important low-energy excitation
such as phonons or mid-IR plasmons. Here we adapt a conventional STEM-EELS
system to probe energy loss down to 100 meV, and apply it to map phononic
states in h-BN, a representative van der Waals (vdW) material. The h-BN EELS
spectra, surprisingly, depend on the h-BN thickness and the distance of the
electron beam to h-BN flake edges. To explain this observation, we developed a
classical response theory describing the interaction of fast electrons with
(anisotropic) slabs of vdW materials. Theoretical and numerical calculations
perfectly match the experimental h-BN spectra, and reveal that the electron
loss is dominated by the excitation of hyperbolic phonon polaritons, and not of
bulk phonons as often reported. Thus, STEM-EELS offers the possibility to probe
low-energy polaritons in vdW materials, with our theory being of fundamental
importance for interpreting future experiments.
