Fig. 2: Enhancement in X-ray intensities from twisted multilayer graphene and twisted multilayer WS2.
a Illustrates a 20 keV single unshaped electron wavefunction (1-state) propagates toward two carbon atoms aligned along the z-axis with interlayer spacing \({d}_{z}\). b, c Show the colormaps (emission angle \({\theta }_{{k}^{{\prime} }}\) against X-ray energy \({E}_{{k}^{{\prime} }}\)) of the bremsstrahlung differential cross section \({\rm{d}}\sigma /\left({\rm{d}}{\omega }_{{k}^{{\prime} }}{\rm{d}}{\Omega }_{{k}^{{\prime} }}\right)\) for \({d}_{z}\) = 3Å and \({d}_{z}\) = 1 Å, respectively. Similarly, (d) illustrates a 20 keV single-shaped electron wavefunction (6-state, incident angle \({\theta }_{p}\) = 15°) and e, f show the corresponding X-ray emission maps for \({d}_{z}\) = 3 Å and \({d}_{z}\) = 1 Å, respectively. Comparing (c, f) and (b, e), shorter interlayer spacing induces slower fluctuations in the X-ray emission map (with respect to X-ray energy and emission angle). g Depicts a 20 keV electron incident on twisted \({N}_{{\rm{l}}}\)-layer graphene (\({d}_{z}\) = 3 Å). (h, i) Show the output X-ray intensity scales up with increasing \({N}_{{\rm{l}}}\) for both unshaped “1-S” and shaped “6-S” (incident angle \({\theta }_{p}\) = 16.22°) electron wavepackets, at twist angles \({\phi }_{{\rm{Twi}}}\) of 0° (emission angle \({\theta }_{{k}^{{\prime} }}\) = 0°) and 3.7° (\({\theta }_{{k}^{{\prime} }}\) = 54°), respectively. j Illustrates 20 keV electron incident on twisted \({N}_{{\rm{l}}}\)-layer WS2 (\({d}_{z}\) = 6 Å). k, l Show the output X-ray intensity scales up with increasing \({N}_{{\rm{l}}}\) for both “1-S” and “6-S” (\({\theta }_{p}\) = 15.77°) electron wavepackets, at \({\phi }_{{\rm{Twi}}}\) of 0° (\({\theta }_{{k}^{{\prime} }}\) = 0°) and 3° (\({\theta }_{{k}^{{\prime} }}\) = 60°), respectively.
