In this paper, we present a three-dimensional one-step photoemission model that can be used to calculate the quantum efficiency and momentum distributions of electrons photoemitted from ordered single-crystal surfaces close to the photoemission threshold. Using Ag(111) as an example, we show that the model can not only calculate the quantum efficiency from the surface state accurately without using any ad hoc parameters, but also provides a theoretical quantitative explanation of the vectorial photoelectric effect. This model in conjunction with other band structure and wave function calculation techniques can be effectively used to screen single-crystal photoemitters for use as electron sources for particle accelerator and ultrafast electron diffraction applications.

Bose condensation has shaped our understanding of macroscopic quantum phenomena, having been realized in superconductors, atomic gases, and liquid helium. Excitons are bosons that have been predicted to condense into either a superfluid or an insulating electronic crystal. Using the recently developed technique of momentum-resolved electron energy-loss spectroscopy (M-EELS), we studied electronic collective modes in the transition metal dichalcogenide semimetal 1T-TiSe2 Near the phase-transition temperature (190 kelvin), the energy of the electronic mode fell to zero at nonzero momentum, indicating dynamical slowing of plasma fluctuations and crystallization of the valence electrons into an exciton condensate. Our study provides compelling evidence for exciton condensation in a three-dimensional solid and establishes M-EELS as a versatile technique sensitive to valence band excitations in quantum materials.