Probing low-energy hyperbolic polaritons in van der Waals crystals with an electron microscope

Abstract

Van der Waals materials exhibit intriguing structural, electronic, and photonic properties. Electron energy loss spectroscopy within scanning transmission electron microscopy allows for nanoscale mapping of such properties. However, its detection is typically limited to energy losses in the eV range—too large for probing low-energy excitations such as phonons or mid-infrared plasmons. Here, we adapt a conventional instrument to probe energy loss down to 100 meV, and map phononic states in hexagonal boron nitride, a representative van der Waals material. The boron nitride spectra depend on the flake thickness and on the distance of the electron beam to the flake edges. To explain these observations, we developed a classical response theory that describes the interaction of fast electrons with (anisotropic) van der Waals slabs, revealing that the electron energy loss is dominated by excitation of hyperbolic phonon polaritons, and not of bulk phonons as often reported. Thus, our work is of fundamental importance for interpreting future low-energy loss spectra of van der Waals materials.

Energy loss spectrum and surface modes of two-dimensional black phosphorus

“…The analytical analysis was performed in the manner of nonretarded approximation. Similar analysis of the electron energy loss probability of uniaxial thin films has been performed for graphite [25,26] and hexagonal boron nitride [27], in which the theoretical results are in good agreement with the experimental measurements. We started with separate calculations of the guided modes, bulk loss, and Begrenzungseffekt.…”

Probing Polaritons in 2D Materials

“…f) Typical spectra acquired on h‐BN with ZLP width of 46 meV where phonon polariton was probed. Reproduced with permission . Copyright 2017, Springer Nature.…”

“…Decreasing the width of ZLP would help overcome this problem. Recently, Govyadinov et al narrowed the ZLP width of a conventional EELS‐TEM down to below 50 meV and probed phonon polaritons in hBN at a meV energy level (Figure f). As high‐resolution EELS (HREELS) has an intrinsically smaller energy resolution than EELS‐TEM, it is suitable for detecting signals at low energy levels .…”

“…The in situ background subtraction enables highly sensitive infrared spectroscopy so that the weak absorption of polaritons in monolayer graphene and h‐BN layers can be detected . The development of high‐resolution electron energy loss spectroscopy (EELS) has enabled the detection of h‐BN phonon polaritons around 100 meV …”

Phonon Polaritons and Hyperbolic Response in van der Waals Materials

“…In this method, the additional momentum is provided by Mie scattering of light from the subdiffractional resonators. The properties of the polaritons can be obtained from the optical transmission/reflection spectroscopy or electron energy loss spectroscopy where spectral resonances are determined by size and shape of the nanostructures.…”