Abstract
The photoluminescence (PL) spectrum of transition-metal dichalcogenides (TMDs) shows a multitude of emission peaks below the bright exciton line, and not all of them have been explained yet. Here, we study the emission traces of phonon-assisted recombinations of indirect excitons. To this end, we develop a microscopic theory describing simultaneous exciton, phonon, and photon interaction and including consistent many-particle dephasing. We explain the drastically different PL below the bright exciton in tungsten- and molybdenum-based materials as the result of different configurations of bright and momentum-dark states. In good agreement with experiments, our calculations predict that WSe2 exhibits clearly visible low-temperature PL signals stemming from the phonon-assisted recombination of momentum-dark K–K′ excitons.
Highlights
The photoluminescence (PL) spectrum of transitionmetal dichalcogenides (TMDs) shows a multitude of emission peaks below the bright exciton line, and not all of them have been explained yet
The large variety of low-temperature emission features at energies below the bright exciton resonance indicates the existence of bound exciton configurations, such as trions, biexcitons,[1−6] and trapped excitons,[7,8] but could result from the indirect recombination of momentum-dark exciton states.[9−16] The radiative decay of a momentum indirect electron−hole pair requires the simultaneous interaction with a phonon to fulfill the momentum conservation and is very inefficient compared to the direct recombination of an exciton with zero center-of-mass momentum
Several theoretical and experimental studies have demonstrated that in tungsten-based monolayer materials, intervalley excitons are located below the optically bright exciton,[15,19−24] and recent experimental PL studies on hBNencapsulated tungsten diselenide have revealed a multitude of low-temperature emission peaks whose microscopic origin still needs to be clarified.[3−5,9]
Summary
The second part of eq 2 containing phonon-assisted decay channels agrees with luminescence formulas derived in previous studies[31,32] for optical phonon replicas in the polaron picture. We have used general compound indices for the excitons allowing to include phonon-assisted transitions involving other exciton states as the ones studied in this work, such as phonon-mediated spin-flip transitions and layer-hybridized Moire excitons as well as localized/charge trapped excitons. Letter which can enable further bound many-particle states, such as biexcitons or trions. The latter gives rise to well studied lowtemperature PL features[1−5,57] below the bright exciton
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