Cross-over from Trion-hole Complex to Exciton Polaron for n-doped Two-dimensional Semiconductors

We study the excitation spectra of n-doped two-dimensional semiconductors due to the absorption of a photon. Because of the interaction between the photocreated exciton and the Fermi sea electrons, exotic new states can emerge. We show that an exciton-single-pair complex can exist by only keeping single electron-hole pair excitations in the Fermi sea. This 4-body complex behaves like a Fermi-sea hole weakly bound to a trion for k_F a_x << 1, where k_F is the Fermi wave-vector and a_x the exciton Bohr radius. The oscillator strength of photo-absorption associated with this trion-hole bound state increases as k_F increases. As k_F continues to increase, the feature of trion-hole bound state becomes unrecognizable, while the exciton state dressed by scattered electron-hole pairs (which can be interpreted as an exciton-polaron) becomes more pronounced. The evolution of the excitation spectra of these 4-particle coupled states (one exciton and one Fermi-sea electron-hole pair) as k_F increases reveals the cross-over from trion-hole resonance to exciton-polaron resonance, which is associated with the internal reconfiguration of the 4-body complex in the presence of the Fermi sea.