Charged excitons in monolayer WSe$_2$: experiment and theory

Abstract: Charged excitons, or X$^{\pm}$-trions, in monolayer transition metal dichalcogenides have binding energies of several tens of meV. Together with the neutral exciton X$^0$ they dominate the emission spectrum at low and elevated temperatures. We use charge tunable devices based on WSe$_2$ monolayers encapsulated in hexagonal boron nitride, to investigate the difference in binding energy between X$^+$ and X$^-$ and the X$^-$ fine structure. We find in the charge neutral regime, the X$^0$ emission accompanied at lower energy by a strong peak close to the longitudinal optical (LO) phonon energy. This peak is absent in reflectivity measurements, where only the X$^0$ and an excited state of the X$^0$ are visible. In the $n$-doped regime, we find a closer correspondence between emission and reflectivity as the trion transition with a well-resolved fine-structure splitting of 6~meV for X$^-$ is observed. We present a symmetry analysis of the different X$^+$ and X$^-$ trion states and results of the binding energy calculations. We compare the trion binding energy for the $n$-and $p$-doped regimes with our model calculations for low carrier concentrations. We demonstrate that the splitting between the X$^+$ and X$^-$ trions as well as the fine structure of the X$^-$ state can be related to the short-range Coulomb exchange interaction between the charge carriers.

• The paper shows that charge-tunable experiments and effective mass modeling reveal binding energy differences of ~20 meV for X⁺ and ~30 meV for X⁻ trions.
• It quantifies a 6 meV fine structure splitting in the X⁻ trion, attributed to short-range Coulomb exchange interactions.
• The research highlights the critical role of electron-hole interactions and dielectric screening in tuning the optical properties of monolayer WSe₂.

Charged Excitons in Monolayer WSe$_2$: Experiment and Theory

The investigation of charged excitons, or trions, in monolayers of transition metal dichalcogenides (TMDCs) has created a new landscape in the study of optical properties of two-dimensional materials. This paper presents an experimental and theoretical analysis of charged excitons in monolayer tungsten diselenide (WSe$_2$). WSe$_2$ is particularly intriguing due to its strong Coulomb interaction effects, which dominate its optical spectra and contribute to various excitonic phenomena across different temperatures.

Significant experimental observations were made using charge-tunable devices where WSe$_2$ monolayers were encapsulated in hexagonal boron nitride (hBN). The study delineates the differences in binding energies between positive (X$^+$) and negative trions (X$^-$), in addition to resolving the fine structure of the X$^-$ trion. Experimentally, the neutral exciton (X$^0$) was observed alongside an additional peak near the longitudinal optical phonon energy, which notably vanished in reflectivity measurements. This suggests that the X$^0$ dominates the optical responses at specific charge conditions, particularly in the n-doped regime.

The numerical results are noteworthy: the binding energies were determined to be approximately 20 meV for X$^+$ and 30 meV for X$^-$. The fine structure of X$^-$ exhibited a splitting of 6 meV, attributed to short-range Coulomb exchange interactions. These findings concur with theoretical symmetry analyses of trion states, demonstrating that electron-hole exchange interactions are crucial for understanding energy dispersions in these systems.

Furthermore, the paper theorizes that the differences in observed trion binding energies can be related to variations in effective masses and the influence of dielectric screening, which are profound due to the monolayer's reduced dimensionality. This is supplemented by effective mass Hamiltonian models for predicting the binding energy of trions in low carrier concentration regimes. Crucially, the discrepancy in the X$^+$ and X$^-$ binding energies observed experimentally cannot be solely ascribed to mass differences in the carriers but requires consideration of exchange interactions.

The implications of this research are multifaceted. Theoretically, it justifies the need for refined models in calculating exchange interactions to predict trion behavior accurately. Practically, understanding these interactions opens avenues for developments in optoelectronic devices utilizing monolayer TMDCs. With an ongoing appeal in integrating 2D materials with advanced photonics technologies, such insights into trion dynamics could drive innovations in designing materials with bespoke optical properties. Future research could explore these interactions under varied dielectric environments or in combination with external perturbations like magnetic or electric fields, thereby enriching the understanding of 2D excitonic systems.