Exciton broadening and band renormalization due to Dexter-like intervalley coupling

Abstract

A remarkable property of atomically thin transition metal dichalcogenides (TMDs) is the possibility to selectively address single valleys by circularly polarized light. In the context of technological applications, it is very important to understand possible intervalley coupling mechanisms. Here, we show how the Dexter-like intervalley coupling mixes A and B states from opposite valleys leading to a significant broadening of the B1s exciton. The effect is much more pronounced in tungsten-based TMDs, where the coupling excitonic states are quasi-resonant. We calculate a ratio , which is in good agreement with the experimentally measured value of . In addition to the broadening effect, the Dexter-like intervalley coupling also leads to a considerable energy renormalization resulting in an increased energetic distance between A1s and B1s states.

Theory of Exciton–Exciton Interactions in Monolayer Transition Metal Dichalcogenides

“…where represents the valley opposed to ξ , i.e., = K′ for ξ = K. The small deviations from the band edges have been omitted in the Bloch functions since they are negligible compared with the distance between the corners of the hexagonal Brillouin zone. These interactions have been introduced as the k ‐space equivalent of the Dexter transfer . For large momentum transfer on the order of the reciprocal lattice vector the Rytova–Keldysh potential is not valid anymore and the effective screening must be adapted to density functional theory calculations …”

Ultrafast dynamics in monolayer transition metal dichalcogenides: Interplay of dark excitons, phonons, and intervalley exchange

“…In this Letter, we study the ultrafast intervalley transfer and relaxation dynamics including simultaneous intervalley exchange and phonon scattering and discuss their role for experimentally observed bleaching in transient pump-probe spectra: After optical excitation of the A transition, a significant bleaching at the B transition was observed. [18][19][20][21] Since the energy of the probed B exciton is hundreds of meV larger [9] compared to the A exciton this type of response comes as a surprise. In particular the helicity resolved data in WS 2 show that the bleaching of the B transition occurs not only in the unpumped valley but also within the pumped valley which, without considering further interactions, can only be attributed to an ultrafast spin flip of the electron [21] or to a mixture of A and B exciton states [22].…”

“…In particular the helicity resolved data in WS 2 show that the bleaching of the B transition occurs not only in the unpumped valley but also within the pumped valley which, without considering further interactions, can only be attributed to an ultrafast spin flip of the electron [21] or to a mixture of A and B exciton states [22]. Interestingly, it was found that the bleaching of the B exciton in the unpumped valley rises faster compared to the pumped valley after optical excitation of the A transition [19][20][21].…”

“…This results in two distinct optical transitions at the K (K ) point where the energetically lower (higher) is called the A (B) transition [9]. pumped valley couples directly to the B exciton in the unpumped valley, whereas the B exciton in the pumped valley is driven through intervalley exchange coupling between B excitons [19,20]. However, so far, only rough estimates for the coupling strength are avilable [19,20].…”

“…pumped valley couples directly to the B exciton in the unpumped valley, whereas the B exciton in the pumped valley is driven through intervalley exchange coupling between B excitons [19,20]. However, so far, only rough estimates for the coupling strength are avilable [19,20]. (c) Beyond intervalley coupling also intravalley exchange coupling leads to an exciton-state mixing between A and B excitons but no polarization selective study of this effect is known yet [22].…”