Super-oscillating Electron Wave Functions with Sub-diffraction Spots

Almost one and a half centuries ago, Ernst Abbe [1] and shortly after Lord Rayleigh [2] showed that when an optical lens is illuminated by a plane wave, a diffraction-limited spot with a radius 0.61*lambda/sin(alpha) is obtained, where lambda is the wavelength and alpha is the semi-angle of the beam's convergence cone. However, spots with much smaller features can be obtained at the focal plane when the lens is illuminated by an appropriately structured beam. Whereas this concept is known for light beam, here, we show how to realize it for massive-particle wave function of a free electron. We experimentally demonstrate an electron central spot of radius 106 pm, which is more than two times smaller than the diffraction limit of the experimental setup used. In addition, we demonstrate that this central spot can be structured by adding orbital angular momentum to it. The resulting super-oscillating vortex beam has a smaller dark core with respect to the regular vortex beam. This new family of electron beams having hot-spots with arbitrarily small features and tailored structure can be useful for studying electron-matter interactions with sub-atomic resolution.