  We propose a robust scheme of studying the strong interactions between free
electrons and photons using topological photonics. Our study reveals that the
topological corner state can be used to enhance the interaction between light
and a free electron significantly. The quality factor of the topological cavity
can exceed 20 000 and the corner state has a very long lifetime even after the
pump pulse is off. And thus, the platform enables us to achieve a strong
interaction without the need for zero delay and phase matching as in
traditional photon-induced near-field electron microscopy (PINEM). This work
provides the new perspective that the topological photonic structures can be
utilized as a platform to shape free electron wave packets, which facilitates
the control of quantum electrodynamical (QED) processes and quantum optics with
free electrons in the future.
