Free electron topological bound state induced by light beam with a twisted wavefront

Abstract: Recent advances in ultrafast electron emission, microscopy, and diffraction have demonstrated a remarkable ability to manipulate free electrons with quantum coherence using light beams. Here, we present a framework for exploring free electron quantum number in ultrafast electron-light interactions. We derive an explicit Jackiw-Rebbi solution for a low-energy free electron wavefunction subjected to a spatiotemporally twisted laser field, resulting in a flying topologically protected bound state with a quantum number of e/2 - termed a "half-electron". This flying bound state is dispersion-free due to its topological nature. We demonstrate the topological confinement and pair generation mechanism of half-electrons in free space, expanding their domain beyond the topological states typically found in solids and photonics. This advancement enhances our understanding of emulating exotic quantum and topological effects with low-energy free electrons.