Fig. 1: Tailoring bremsstrahlung via electron waveshaping and twisted bilayer vdW materials.
a Illustrates the bottom view of a twisted bilayer graphene which the two atomic layers (lies in the xy-plane) are twisted in opposite orientation at twist angle \({\phi }_{{\rm{twi}}}\). b Depicts a 20 keV single-shaped electron wavefunction (6-state, incident angle \({\theta }_{p}\) = 8.03°) propagating in the z-axis toward a twisted bilayer graphene. c Shows the shaped electron spatial profile (probability distribution function \({\Psi }_{p}^{\dagger }{\Psi }_{p}\)) with periodic patterns, where solid (dashed) gray circles denoting the projections of effective carbon atoms in the first (second) layer. The output 15 keV X-ray angular profiles (differential cross section \({\rm{d}}\sigma /\left({\rm{d}}{\omega }_{{k}^{{\prime} }}{\rm{d}}{\Omega }_{{k}^{{\prime} }}\right)\)) are shown in (d, e) for twist angles of 0° and 7.4°, respectively. f Illustrates the bottom view of a twisted bilayer WS2 and g Depicts a 20 keV single-shaped electron wavefunction (6-state, incident angle \({\theta }_{p}\) = 9.42°) propagating in the z-axis towards a twisted bilayer WS2. Its spatial profile is shown in (h) where solid (dashed) purple and yellow circles denoting the projections of effective tungsten and sulfur atoms in the first (second) layer, respectively. The output 15 keV X-ray angular profiles (differential cross section \({\rm{d}}\sigma /\left({\rm{d}}{\omega }_{{k}^{{\prime} }}{\rm{d}}{\Omega }_{{k}^{{\prime} }}\right)\)) are shown in (i, j) for twist angles of 0° and 4.9°, respectively. For different twist angle, shaped electron incident on bilayer vdW materials can emit X-ray with either unidirectionality (d, i) or enhanced intensity (e, j), compared to unshaped electron cases.
