  In pursuit of quantum advancements across disciplines, a bright and coherent
electron source is expected to be a cornerstone of diverse applications
including electron microscopy, laser accelerators, and free electron lasers.
Current cathodes, such as cold field and photoemission, can generate
high-quality electron beams with different cathode materials, geometric
configurations, and laser excitation profiles, but their maintenance of both
quantum coherence and high beam brightness suffers from the space-charge
repulsion of many electrons. Here, we propose a new mechanism to provide
collective emission of coherent electrons based on Auger photoemission. Our
approach leverages a photon-induced four-level Auger process that necessitates
a combination of photoemission and Auger recombination. The Auger electrons,
energized through a recycling process of photoelectrons, emit collectively into
the vacuum as secondary electrons. We compare coherent and incoherent Auger
photoemission, identifying that the working condition of the coherent
photoemission requires population inversion, akin to the four-level laser
system. Our work provides insights for experimental realization and
nanofabrication of Auger photocathodes, addressing a critical need in advancing
quantum technologies relating to correlated coherent sources.
