Enhanced Scattering between Electrons and Exciton-Polaritons in a Microcavity

The interplay between strong light-matter interactions and charge doping represents an important frontier in the pursuit of exotic many-body physics and optoelectronics. Here, we consider a simplified model of a two-dimensional semiconductor embedded in a microcavity, where the interactions between electrons and holes are strongly screened, allowing us to develop a diagrammatic formalism for this system with an analytic expression for the exciton-polariton propagator. We apply this to the scattering of spin-polarized polaritons and electrons, and show that this is strongly enhanced compared with exciton-electron interactions. As we argue, this counterintuitive result is a consequence of the shift of the collision energy due to the strong light-matter coupling, and hence this is a generic feature that applies also for more realistic electron-hole and electron-electron interactions. We furthermore demonstrate that the lack of Galilean invariance inherent in the light-matter coupled system can lead to a narrow resonancelike feature for polariton-electron interactions close to the polariton inflection point. Our results are potentially important for realizing tunable light-mediated interactions between charged particles.

Figure 1

(a) Dyson equation for the dressed photon propagator (thick wavy line) in terms of the bare propagator (thin wavy line) and the self energy (shaded ellipse). The self energy consists of the two terms in Eq. (3), where the thin lines with arrows are fermion propagators and the shaded rectangle is the electron-hole $T$ matrix defined in Eq. (4). Black dots represent the light-matter coupling $g$. (b) Polariton propagator (double lines with an arrow) given by repeated interactions between excitons, dressed photons, and electron-hole pairs. (c) Polariton-electron scattering, as encoded in the polariton-electron $T$ matrix (shaded square). Black, white, and dashed circles represent electrons, holes, and polaritons, respectively.

Figure 2

Polariton-electron interaction strength as a function of photon-exciton detuning, taking $\mathrm{\Omega }/{ϵ}_B=0.025$ as in a ${\mathrm{MoSe}}_2$, ${\mathrm{MoS}}_2$, or ${\mathrm{WSe}}_2$ monolayer. The exact diagrammatic calculation (blue solid line) compares well with the off-shell exciton-electron scattering approximation in Eq. (10) (gray dash-dotted line). Inset: the Born approximation (gray dashed line) deviates from the exact calculation in a large parameter region.

Figure 3

Polariton-electron scattering $T$ matrix at finite momentum. Blue (yellow) lines correspond to $T_{eP}(Q)$ with $\mathrm{\Omega }/{ϵ}_B=0.2$ (0.05), where the solid and dashed lines are $\delta =-\mathrm{\Omega }$ and $\mathrm{\Omega }$, respectively, such that the Hopfield coefficients are the same for the two negative (positive) detuning lines. The thin purple dashed line is the low-energy exciton-electron $T$ matrix $T_{eX}(Q)=(3\pi /m)/[-\ln (-3{\epsilon }_Q/2{ϵ}_1)]$.