Abstract
The effects of the electron-phonon interaction on optical excitations can be understood in terms of exciton-phonon coupling, and require a careful treatment in low-dimensional materials with strongly bound excitons or strong electron-hole interaction in general. Through phonon absorption and emission processes, the optically accessible excitons are scattered into otherwise optically dark finite-momentum exciton states. We derive a practical expression for the phonon-induced term of the exciton self-energy (denoted as the exciton-phonon self-energy) that gives the temperature dependence of the optical transition energies and their lifetime broadening resulting from the exciton's interaction with the phonons. We illustrate this theory on a two-dimensional model, and show that our expression for the exciton-phonon self-energy differs qualitatively from previous expressions found in the literature that neglect the exciton binding or electron-hole correlations.
Highlights
A wealth of two-dimensional and nanocrystalline materials with interesting optical properties have been studied in recent years, including transition-metal dichalcogenides, layered heterostructures, and halide perovskites [1,2,3,4,5,6,7]
The optical excitations lead to the formation of strongly bound electron-hole pair states known as excitons. Many of their useful opto-electronic properties depend on the scattering dynamics and diffusion of the excitons [8,9,10,11,12,13,14]. This dynamics is governed by several processes: the interaction of excitons with defects, the exciton-exciton interaction, and the exciton-phonon interaction
We have derived a rigorous expression for the exciton-phonon coupling self-energy to lowest order in the electron-phonon interaction and in the limit of low exciton density
Summary
A wealth of two-dimensional and nanocrystalline materials with interesting optical properties have been studied in recent years, including transition-metal dichalcogenides, layered heterostructures, and halide perovskites [1,2,3,4,5,6,7]. The electron-phonon renormalization and broadening of the band structure is computed before solving the BSE This method does not, describe correctly the process where excitons scatter into finite-momentum bound states, which is necessary to enforce energy conservation. Recent methods formally achieved a proper description of exciton dynamics with exciton-phonon scattering amplitude deduced from Fermi’s golden rule using exciton-phonon coupling matrix elements [43,44,45,46] This approach enforces energy conservation, and is consistent with the theory presented in this paper, as well as other methods derived from many-body perturbation theory [47]. Several mathematical details of the derivation can be found in Ref. [50]
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