[Paper Review] Identifying optical signatures of momentum-dark excitons in transition metal dichalcogenide monolayers

Jessica Lindlau, Cédric Robert+13 more|arXiv (Cornell University)|Oct 3, 2017

2D Materials and Applications17 citations

TL;DR

This paper proposes that unidentified photoluminescence (PL) peaks in transition metal dichalcogenide (TMD) monolayers arise from phonon-assisted radiative recombination of momentum-dark excitons—excitons formed between electrons in one valley and holes in another. By modeling acoustic and optical phonon sidebands of these dark excitons, the authors achieve a quantitative fit to experimental PL spectra, resolving long-standing ambiguities in TMD optical response and explaining intense, unassigned peaks as replicas of momentum-dark states rather than defect-related features.

ABSTRACT

Transition metal dichalcogenide (TMD) monolayers (MLs) exhibit rich photoluminescence spectra associated with interband optical transitions of direct-gap semiconductors. Upon absorption of photons, direct excitons with zero center-of-mass momentum are formed by photo-excited electrons in the conduction band and the respective unoccupied states in the valence band of the same valley. Different spin configurations of such momentum-direct excitons as well as their charged counterparts provide a powerful platform for spin-valley and microcavity physics in two-dimensional materials. The corresponding spectral signatures, however, are insufficient to explain the main characteristic peaks observed in the photoluminescence spectra of ML TMDs on the basis of momentum- extit{direct} excitons alone. Here, we show that the notion of momentum- extit{indirect} excitons is important for the understanding of the versatile photoluminescence features. Taking into account phonon-assisted radiative recombination pathways for electrons and holes from dissimilar valleys, we interpret unidentified peaks in the emission spectra as acoustic and optical phonon sidebands of momentum-dark excitons. Our approach will facilitate the interpretation of optical, valley and spin phenomena in TMDs arising from bright and dark exciton manifolds.

Motivation & Objective

• To resolve the long-standing ambiguity in photoluminescence (PL) spectra of transition metal dichalcogenide (TMD) monolayers, where some intense peaks cannot be explained by bright excitons alone.
• To investigate the role of momentum-dark excitons—excitons with non-zero center-of-mass momentum—whose radiative decay is normally forbidden but can occur via phonon assistance.
• To provide a unified explanation for unassigned PL features in WSe2 and WS2 monolayers by incorporating phonon sidebands of momentum-dark excitons into spectral models.
• To improve the interpretation of optical, valley, and spin phenomena in TMDs by distinguishing contributions from bright and dark excitonic manifolds.
• To validate the model using high-quality hBN-encapsulated TMD monolayers with tunable charge and reduced spectral broadening.

Proposed method

• The study models photoluminescence spectra as a sum of zero-phonon lines (ZPLs) of momentum-direct excitons (X, D) and phonon sidebands of momentum-dark excitons formed between electrons in Q-pockets or K′-valleys and holes in the K-valley.
• Phonon-assisted recombination pathways are calculated using in-plane transverse (TA) and longitudinal (LA) acoustic phonons, and optical phonons, with momentum conservation enforced via the q-vector of the phonon mode.
• A fitting procedure is applied to experimental PL data from WSe2 and WS2 monolayers, adjusting parameters such as the energy of the Q-exciton level (ΔXQ), exchange splitting, and phonon coupling strengths to match observed spectra.
• The model assumes identical linewidths for all momentum-dark excitons, though this is acknowledged as a simplification that may affect quantitative accuracy.
• Theoretical estimates of phonon modes and band structures are used to constrain the energy positions and coupling strengths, with validation from cryogenic spectra of bilayer WSe2 and MoSe2-WSe2 heterobilayers.
• Second- and higher-order phonon processes are considered but restricted to combinations with net momentum matching Q or K points, based on initial electron valley and phonon emission.

Experimental results

Research questions

• RQ1 Why do some intense photoluminescence peaks in TMD monolayers remain unassigned despite known bright exciton contributions?
• RQ2 Can phonon-assisted recombination explain the spectral features attributed to momentum-dark excitons in WSe2 and WS2?
• RQ3 What is the energy position of the momentum-dark Q-exciton relative to the bright X and D excitons in WSe2 and WS2 monolayers?
• RQ4 How do acoustic and optical phonon sidebands contribute to the overall PL spectrum, particularly in the presence of spin-forbidden excitonic states?
• RQ5 To what extent can the inclusion of momentum-dark excitons resolve ambiguities in deconvoluting neutral and charged exciton contributions in TMD PL spectra?

Key findings

• The first scenario, where the Q-exciton level lies 19 meV below the bright exciton (ΔXQ ≈ 19 meV), provides a better fit to the PL spectrum of WSe2 monolayers than placing it above the bright state.
• In WS2, the second scenario—where the Q-exciton is positioned between the D and X states—yields a better fit and explains the first weak PL peak below X as an acoustic phonon sideband of the Ql-exciton.
• The model successfully reduces the previously large and unphysical exchange splitting between X and K′u states observed in earlier fits, bringing it into better alignment with theoretical predictions.
• Optical phonon sidebands of momentum-dark excitons are found to merge into the most intense PL peak between X and D in WS2, explaining its high intensity without invoking defect localization.
• The model's qualitative and quantitative agreement with experimental spectra is robust, even with simplifying assumptions such as uniform linewidths across momentum-dark excitons.
• The study confirms that momentum-dark excitons are key to explaining the complex PL features in TMD monolayers, particularly in WSe2 and WS2, and provides a framework for interpreting future high-precision spectroscopy.