  This manuscript presents, to our knowledge, the first fully ab initio
many-body photoemission framework to predict the transverse momentum
distributions and the mean transverse energies (MTEs) of photoelectrons from
single-crystal photocathodes. The need to develop such a theory stems from the
lack of studies that provide complete understanding of the underlying
fundamental processes governing the transverse momentum distribution of
photoelectrons emitted from single crystals. For example, initial predictions
based on density-functional theory calculations of effective electron masses
suggested that the (111) surface of PbTe would produce very small MTEs ($\leq$
15 meV), whereas our experiments yielded MTEs ten to twenty times larger than
these predictions, and also exhibited a lower photoemission threshold than
predicted. The ab initio framework presented in this manuscript correctly
reproduces the magnitude of the MTEs from our measurements in PbTe(111) and
also the observed photoemission below the predicted threshold. Our results show
that photoexcitations into bulk-like states and coherent, many-body
electron-photon-phonon scattering processes, both of which initial predictions
ignored, indeed play important roles in photoemission from PbTe(111). Finally,
from the lessons learned, we recommend a procedure for rapid computational
screening of potential single-crystal photocathodes for applications in
next-generation ultrafast electron diffraction and X-ray free-electron lasers,
which will enable new, significant advances in condensed matter research.
