What is the signature of a trion in photoemission?

Abstract

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.

Figures (3)

• Figure 1: Schematic of two trion modes and photoemission processes considered in this paper. (a) The positive trion, in which there is only one electron which can be photoemitted and detected by ARPES. (b) The negative trion mode, with two electrons, either of which can be photoemitted in ARPES, leaving behind either an intervalley K-K' or intravalley K-K exciton.
• Figure 2: Comparison of signals from the lowest energy optically active exciton and positive trion in the one-electron emission spectrum in tr-ARPES of monolayer MoS2. (a) ARPES heatmap of the exciton at $\vb{Q} = 0$ and (b) the trion at $\vb{P} = \vb{w}$. The momentum path is along K-K'. The x-axis corresponds to $\vb{k}$, the momentum of the photoemitted electron. The solid black curves are the valence and conduction bands. (a) The exciton plot. The red dashed curve highlights the dispersion of the maximum ARPES intensity. The panel on the right is an energy distribution curve (EDC) showing the intensity along the gray dashed vertical line in the heatmap. (b) The trion plot. The red dashed curve is a replica of the valence band, which approximately follows the dispersion of the maximum ARPES intensity. The orange dashed curve follows the upper edge of the signal and has an effective mass of $2m_{\text{h}}$. The two panels on the right correspond to the EDC at K (dark gray dashed line) and away from K (light gray dotted line). (c,d) Similar to (a,b), but for the $\vb{Q} = 0.2 \vb{w}$ exciton and the $\vb{P} = 1.2 \vb{w}$ trion, respectively. The horizontal dotted line in all the four heatmaps give the energy of the global maxima of the ARPES intensity.
• Figure 3: One-electron photoemission spectrum from the lowest negative trion in tr-ARPES of monolayer MoS2. The signal at the K valley is from the dispersion of the A-series of excitons with $\vb{Q} \approx \mathrm{K}$ (i.e. the intervalley exciton), while the signal in the K' valley is from the A-series of excitons with $\vb{Q} \approx 0$ (i.e. the intravalley exciton). The exciton dispersion is taken from Ref. qiu2015nonanalyticity. The orange dashed lines trace the exciton bands, the highest ones corresponding to 1s, 2p, and 2s exciton states.