Retardation effects on exciton-polariton dispersions and radiative lifetimes in quasi-two-dimensional materials

It is well known that the inclusion of retardation effects in the interaction of excitons and photons leads to a renormalization of the exciton dispersion and the formation of exciton-polaritons. In bulk materials the exciton center-of-mass momentum and photon momentum are fully conserved in their interaction, leaving the radiative lifetime of the excitation unchanged and infinite. However, in quasi-two-dimensional (q2D) materials only the in-plane projection of the photon's momentum is conserved in the interaction with excitons. To capture this effect, we employ a q2D generalization of the retarded Bethe-Salpeter equation using a fully relativistic electron-hole exchange interaction which accounts for this modified momentum conservation condition. Applying our formalism to monolayer MoTe2, we present the first ab initio calculations of q2D exciton-polariton radiative lifetimes as well as real-space visualizations of the matter component of the exciton-polariton wavefunction. We find that the finite radiative lifetimes we compute lead to a broadening of the exciton dispersion as the retarded long-range exchange interaction becomes complex inside the light cone. This result helps settle a long-standing question on the linear and parabolic dispersive behavior of bright excitons in monolayer TMDs inside the light cone. Lastly, we comment on the role of local field effects and q2D photon confinement for the non-radiative branch of the exciton dispersion.