Probing low-energy hyperbolic polaritons in van der Waals crystals with   an electron microscope
  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. 
Alexander A. Govyadinov, Andrea Kone\v{c}n\'a, Andrey Chuvilin, Sa\"ul   V\'elez, Irene Dolado, Alexey Y. Nikitin, Sergei Lo...
cond-mat.mes-hall cond-mat.mtrl-sci