Quantum Many-Body Light-Matter Interaction in 2D Materials

The strong light-matter interaction and strong Coulomb interaction in 2D materials, in particular in transition metal dichalcogenides (TMDs), give rise to a rich set of many-body highly correlated quantum states of light and matter. The most prominent of these states are excitons, trions, bi-excitons and their respective polaritons. The optical emission and absorption spectra of doped 2D TMDs shows two prominent peaks that have been traditionally labeled as the exciton and the trion peak. Until very recently, and for over several past decades, a trion was considered to be a charged bound state of two electrons and one hole (or two holes and one electron). This concept of a trion could neither explain the variation of the trion linewidth and binding energy with the doping density nor the experimental observation of polaritons involving trions. Thus, a revision in the concept of a trion was required. In this talk, we will discuss the modern picture of excitons and trions, and their polaritons, in doped 2D materials that has emerged in the last several years [1-3]. In an electron doped 2D material, an exciton is not a good eigenstate of the Hamiltonian. A two-body exciton gets coupled with four-body excitations consisting of two electrons in the conduction band, one hole in the valence band and one hole in the conduction band (what is also called the Fermi hole) as a result of the Coulomb interaction between the exciton and the electron density. The four-body trion states have no direct optical matrix elements with the material ground state. The contribution to the material optical conductivity from these four-body trion states results almost entirely from their Coulomb coupling to the exciton states [1]. Neither the exciton and nor the four-body trion are good eigenstates of the Hamiltonian in doped 2D materials. Supersposition states of excitons and four-body trions [1], also called exciton-polaron states [2-3], are good eigenstates. The exciton-polaron states resemble the Fermi-polaron states observed in cold atomic gases [4]. The exciton-trion superposition states can quantitatively explain all the prominent features experimentally observed in the optical absorption spectra of 2D materials, including the observation of two prominent absorption peaks and the variation of their energy splittings, spectral strengths, and spectral linewidths with the doping density. The strong light-matter coupling between photons and excitons inside an optical microcavity and the strong Coulomb coupling between the four-body trions and the excitons result in robust exciton-trion-polaritons (or exciton-polaron-polaritons) that are highly correlated states of light and matter [5-6]. We present experimental results on exciton-trion-polaritons states and their energy dispersion [6]. These polariton states display three energy bands and their experimentally measured energy-momentum dispersion is well described by the theory described here. The talk will also present the practical applications of these unusual polariton states in novel devices such as highly efficient light modulators and switches. Going further in the hierarchy of many body states, biexcitons and charged biexcitons have also been experimentally observed in 2D materials. We will show that in an exciton gas, neither the excitons nor the biexcitons are good eigenstates but exciton-biexciton superposition states, to the first level of approximation in the exciton density, are good eigenstates and correspond to the excitations observed in experiments. Finally, we will show that the phenomenology of charged biexciton states is similar to that of the charged exciton states.
[1] F. Rana, et al., Phys. Rev. B, B 102, 085304 (2020).
[2] M. Sidler et al., Nat. Phys., 13, 255 (2016).
[3] D. K. Efimkin et al., Phys. Rev. B, 95, 035417 (2017).
[4] F. Scazza et al., Atoms, 10(2), 55 (2022).
[5] F. Rana, Phys. Rev. Lett., 126, 127402 (2021).
[6] O. Koksal et al., Phys. Rev. Res. 3, 033064 (2022).