Excitation and probing of hyperbolic phonon polaritons in hexagonal boron nitride structures by fast electrons
Authors: Konečná Andrea , Govyadinov Alexander , Chuvilin Andrey , Dolado Irene , Vélez Saül , Aizpurua Javier , Hillenbrand Rainer 
Published: December 2016

Hexagonal boron nitride (hBN) is a representative material of a wide class of two‐dimensional systems in which individual atomic layers are only weakly coupled by van der Waals interaction, resulting, among others, in extreme optical anisotropy. The latter gives rise to hBN's hyperbolic phonon polaritons (h‐PhPs), i.e. coupled excitations of optical phonons and light that exhibit hyperbolic dispersion [1, 2] at mid‐infrared (mid‐IR) energies, specifically in the range of 90‐200 meV. Hyperbolic polaritons might be a key to many emerging photonic technologies that rely on nanoscale light confinement and manipulation, such as nanoscale imaging or sensing [3]. Thus, efficient design and utilization of hBN (nano)structures require spectroscopic studies with adequate spatial resolution and energy range.

Electron energy loss spectroscopy (EELS) performed in scanning transmission electron microscope (STEM) is a versatile technique that employs fast electrons as an effective localized electromagnetic probe for spectroscopy with nanoscale spatial resolution. Successfully employed at visible and near‐IR energies, this technique has limited capabilities for mid‐IR spectroscopy primarily due to lack of monochromaticity of the primary electron beam which typically masks low energy excitations under
~
200 meV with the zero loss peak (ZLP) originating from the elastic electron scattering and also limits the spectral resolution to
~
100 meV.

Here we demonstrate that by an optimization of microscope data acquistion and signal processing it is possible to significantly reduce the ZLP width down to 50 meV (with corresponding resolution enhancement), placing mid‐IR spectroscopy within the reach of standard TEM instruments.
To this end, we perform experimental mapping of the spectral signature at an hBN edge. As summarized in Fig. a, we clearly observe the variation in spectral peak position as a function of the electron impact parameter (position of the electron beam with respect to the edge). As revealed by our theoretical analysis, this behavior is the manifestation of polaritonic nature of the induced excitations. Indeed, our developed analytical and numerical models of EELS in structured hyperbolic materials show the existence of multiple EEL peaks depending on the impact parameter (see Fig. b). These peaks are due to the reflection of propagating h‐PhPs from the hBN edge, which proves that fast electrons can and do couple to the hyperbolic polaritons. After mimicking the experimental spectral resolution (via convolution of the calculated spectra with a Gaussian of proper experimental width), we obtain a good agreement with the experimental data (see Fig. c).
Our work provides first steps in understanding polaritonic excitations produced by fast electrons in hyperbolic materials and sets grounds for the rigorous analysis of the observed low‐energy EELS. With the ongoing improvements of STEM‐EELS instrumentation [4], we expect further enhancement of the spectral resolution and an extension of the applicable energy ranges in near future, thus enabling EELS in STEM as a versatile technique for infrared spectroscopy of polaritons.