What is the signature of a trion in photoemission?
Recent advances in time- and angle-resolved photoemission spectroscopy (tr-ARPES) allow for the probing of multiparticle excited-states in reciprocal space. While neutral two-particle excitations (excitons) have been observed in tr-ARPES, signatures of trions -- three-quasiparticle bound states -- have only been probed via optical spectroscopy. Here, we develop a general theory for the ARPES signature of trions in the model system of a monolayer transition metal dichalcogenide (TMD). We simulate the ARPES signals of both positively and negatively charged trions and show that the interaction of the residual holes, or electron and hole, lead to large energy shifts, on the order of the exciton binding energy, compared to the exciton signal. For positive trions, the additional momentum degree of freedom of the residual particles removes any strict lower bound on the photoemission energy, leading to distinctive asymmetric spectral features. For negative trions, the photoemission process causes the tr-ARPES spectrum to reproduce inverted images of the exciton band structure for multiple exciton states, encompassing both spin-allowed and spin-forbidden states, providing a direct momentum-resolved probe of both trion and exciton physics.