Fig. 4: Hot ILX Relaxation.
a Sketch of optically bright ILX formation process following thermal relaxation of hot, momentum dark ILX. The formation process occurs in three steps: (1) After resonant excitation of the AMo transition, the MoSe2 layer is populated by incoherent populations, \({N}_{{{{{{{{\bf{Q}}}}}}}},1s}^{Mo,K}\), (left red parabola) and subsequent phonon-assisted IL hole tunneling leads to the formation of ILX incoherent populations, \({N}_{{{{{{{{\bf{Q}}}}}}}},\mu }^{IL,K}\), with finite momentum Q and also high quantum number μ (right green parabolas) (see Eq. (1) and Eq. (4)). (2) and (3) The distribution of hot ILX lose energy and momentum by scattering on ultrafast timescales with high energy optical phonons and with low energy acoustic phonons on longer timescales. b Snapshots of the normalized momentum-dependent excitonic populations of ILX at different delays overlaid on the Pauli-blocking weights \({D}_{{{{{{{{\bf{Q}}}}}}}}}^{W}\) of the AW (solid purple), with i = W, K, \({i}^{{\prime} }=IL,K\), (see Eq. (3)) and \({D}_{{{{{{{{\bf{Q}}}}}}}}}^{IL}\) of the ILX (solid green), with i = IL, K, \({i}^{{\prime} }=IL,K\) (see Eq. (3)). The distribution in momentum space reflects the different localization of the excitonic wave functions and, thus, the different binding energies of the AW (215 meV) and of the ILX (91 meV). The binding energy of ILX is the offset between the lowest 1s state and the onset of the continuum at Q=0. Following IHT, the population distribution of K − K valley ILX, \({N}_{{{{{{{{\bf{Q}}}}}}}},1s}^{IL,K}\), (lines) is peaked around finite Q values between 2 − 2.5 nm−1, overlapping strongly with AW Pauli-blocking weight. The overlap of the \({N}_{{{{{{{{\bf{Q}}}}}}}},1s}^{IL,K}\) with the ILX Pauli-blocking weight increases as they shift to lower energy and momentum via scattering processes described in (a). Below the energy threshold of 30 meV (gray line) the scattering is mediated only by acoustic phonons as scattering by optical phonons is energetically forbidden.
