EELS Compton Scattering and The Electronic Structure of Materials

Electronic structure is fundamental to a large class of materials phenomena, including mechanical, optical, magnetic and electronic transport properties. Momentum based spectroscopies such as angle resolved photoemission spectroscopy (ARPES), electron-positron annihilation and Compton scattering are traditionally used to measure the electronic structure. Compton scattering in the transmission electron microscope (TEM) was first explored in the 1980s using electron energy loss spectroscopy (EELS) [1]. Despite early success it did not achieve widespread use, largely due to the limitations in EELS spectrometer detector efficiencies, and artefacts arising from Bragg scattering within a crystalline specimen. However, with modern advances in EELS spectrometers as well as computational techniques for modelling dynamical scattering artefacts [2] many of the challenges facing EELS Compton scattering are arguably now resolved. EELS Compton scattering in the TEM provides several benefits over standard X-ray and gamma-ray Compton measurements, such as a higher spatial resolution and the ability to extract useful information from even poly-crystalline materials.<br/><br/>In EELS Compton scattering the incident electron beam undergoes an inelastic collision with individual electrons in the solid. The Compton signal appears as a broad peak in an EELS spectrum acquired at large scattering angles (i.e. high momentum transfer). The width of the Compton profile, which can be as large as several hundred eV, is due to the intrinsic momentum spread of the solid-state electrons. The Compton profile shape is therefore directly related to J(p_z), i.e. the density of solid-state electrons with momentum component p_z along the scattering vector direction. J(p_z) provides a 1D projection of the electronic band structure in reciprocal space. We have applied EELS Compton scattering to examine the electronic structure of bi-layer WS₂ [3], with a twist angle of 18^o between the two layers. EELS Compton scattering is particularly suitable to this problem, since the low dimensional nature of the WS₂ flakes make it difficult or impossible to analyse using conventional methods. The J(p_z) acquired along the 100 reciprocal direction indicates that the electrons are more delocalised in the bi-layer compared to monolayer WS₂. Comparison with density functional theory (DFT) simulations reveal that the delocalization is due to a small amount of electronic charge (i.e. 0.1%) accumulating in the inter-layer region. The inter-layer charge accumulates between overlapping W atoms, thereby screening the ‘wrong’ bonds generated by the twist angle. The charge accumulation is also accompanied by a local dilation of the inter-layer spacing. Time permitting I will also present other examples of EELS Compton scattering that are of interest.<br/><br/>[1] BG Williams, TG Sparrow, RF Egerton, <i>Proc. R. Soc. London A</i>, <b>393</b> (1984) 409.<br/>[2] BG Mendis, A Talmantaite, <i>Microsc. Microanal. </i><b>28</b> (2022) 1971.<br/>[3] A Talmantaite, Y Xie, A Cohen, PK Mohapatra, A Ismach, T Mizoguchi, SJ Clark, BG Mendis, <i>Phys. Rev. B</i> <b>107</b> (2023) 235424.