Structure and dispersion of exciton-trion-polaritons in two-dimensional materials: Experiments and theory

The nature of trions and their interaction with light has remained a puzzle. The composition and dispersion of polaritons involving trions provide insights into this puzzle. Trions and excitons in doped two-dimensional (2D) materials are not independent excitations but are strongly coupled as a result of Coulomb interactions. When excitons in doped 2D materials are also strongly coupled with light inside an optical waveguide, the resulting polariton states are coherent superpositions of exciton, trion, and photon states. We realize these exciton-trion-polaritons by coupling an electron-doped monolayer of 2D material ${\mathrm{MoSe}}_2$ to the optical mode in a photonic crystal waveguide. Our theoretical model, based on a many-body description of these polaritons, reproduces the measured polariton energy band dispersion and Rabi splittings with excellent accuracy. Our work sheds light on the structure of trion states in 2D materials and also on the indirect mechanism by which they interact with light.

Figure 1

(a) The nature of couplings involved in exciton-trion-polaritons in electron-doped two-dimensional (2D) material ${\mathrm{MoSe}}_2$ is depicted. Excitons are optically coupled to the material ground state. Excitons are also coupled to bound trions and unbound trions (exciton-electron scattering states) via Coulomb interactions. Trion states are four-body states consisting of two conduction band (CB) electrons, one valence band (VB) hole, and one CB hole. The trion states have a zero optical matrix element with the material ground state. (b) A coherent exciton-trion-polariton state is pictorially represented as a superposition of exciton, trion, and photon states.

Figure 2

(a) Schematic of the one-dimensional (1D) photonic crystal (PC) waveguide device used to realize exciton-trion-polaritons. The device consists of a ${\mathrm{MoSe}}_2$ monolayer (ML) transferred on top of the waveguiding layer. (b) Band structure of the bare PC waveguide (without the ${\mathrm{MoSe}}_2$ ML) is plotted as a function of the in-plane momenta. The transverse-electric (TE)-polarized waveguide mode used to realize exciton-trion-polaritons is indicated by the arrow. (c) Calculated electric field intensity of the TE-polarized waveguide mode (normalized with respect to its maximum value) is plotted for zero in-plane momentum. (d) The ${\mathrm{MoSe}}_2$ ML is characterized using surface-normal photoluminescence (PL) (left plot) and reflection (bottom right plot) spectroscopies for light polarized in the $x$ direction. Zero-momentum energy of the TE-polarized waveguide mode is indicated by the dashed line in the PL spectra (left plot). The reflection spectra shown are normalized to the reflection spectra obtained from a part of the device which had the grating but was not covered with the ${\mathrm{MoSe}}_2$ ML. The optical conductivity (real part) spectrum of the ${\mathrm{MoSe}}_2$ ML, computed using the measured parameters, is also shown (top right plot).

Figure 3

The measured (right) and calculated (left) reflection spectra of the bare photonic crystal (PC) waveguide [without the ${\mathrm{MoSe}}_2$ monolayer (ML)] is plotted as a function of the in-plane momentum $k_{\mathrm{z}}$. The dashed lines are the computed energy-momentum dispersion of the mode. The reflection spectra shown are normalized to the reflection spectra obtained from a part of the device which had no grating and was also not covered with the ${\mathrm{MoSe}}_2$ ML.

Figure 4

The measured (right) and calculated (left) reflection spectra of the polariton device shown in Fig. 2 is plotted as a function of the in-plane momentum $k_{\mathrm{z}}$. The dashed lines are the computed energy-momentum dispersion of the exciton-trion-polaritons. In the calculations, no parameter values were adjusted to fit the data. The reflection spectra show three polariton bands: upper (UP), lower (LP), and middle (MP). The reflection spectra shown are normalized to the reflection spectra obtained from a part of the device which had no grating and was also not covered with the ${\mathrm{MoSe}}_2$ ML. T = 10 K.

Figure 5

The measured photoluminescence (PL) spectra from the polariton device (right) and the computed photon spectral weight of the polariton state (left) are plotted as a function of the in-plane momentum $k_{\mathrm{z}}$. Both spectra are normalized with respect to their peak values. As expected from thermal relaxation, most of the PL emerges from the lower two polariton bands [lower (LP) and middle (MP)], and hardly any PL is obtained from the upper (UP) polariton band. T = 10 K.