Distinctive signatures of the spin- and momentum-forbidden dark exciton states in the photo-luminescence of strained WSe2 monolayers under thermalization

Guan-Hao Peng^1*, Ping-Yuan Lo¹, Wei-Hua Li¹, Yan-Chen Huang¹, Chi-Hsuan Lee², Chih-Kai Yang², Shun-Jen Cheng¹

¹Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan
²Graduate Institute of Applied Physics, National Chengchi University, Taipei, Taiwan

* Presenter:Guan-Hao Peng, email:bnm852i@gmail.com

Transition-metal dichalcogenide monolayers (TMDC-MLs) are the two-dimensional semiconductors that possess not only the unique spin-valley locking effect but also the pronounced exciton nature originated from the weak dielectric screening of its low-dimensionality. Their intriguing bright and dark valley-exciton fine structures provide rich physics for the study of the photo-luminescence (PL) behavior of the atomically thick crystals, where the dark excitons can be classified into the spin- and momentum-forbidden one from the optical selection rules. One of the most essential issues in this research field is to identify the energy order of the bright and dark excitons, since the PL intensity is determined by the population of the bright excitons when the system is in thermal equilibrium and it can be significantly affected if there exist some nearby dark exciton levels below or above the bright exciton levels. In TMDC-MLs, the dark excitons with energy lower than the bright excitons have been identified by many theoretical and experimental investigations. However, the study that can directly identify the dark excitons with energy higher than the bright excitons is still absent now. In this work, we present the theoretical investigation of the exciton fine structures and the temperature-dependent time-integrated PL of WSe2-MLs by solving the Bethe-Salpeter equation in the scheme of tight-binding theory established from the first principle density-functional-theory computation. With the supportive model analysis, we reveal that the signature of the quickly rising (slowly descending) PL intensity with increasing the temperature in the low (high) temperature regime is corresponding to the spin-forbidden (highly-degenerate momentum-forbidden) dark excitons with energy lower (higher) than the bright excitons. At last, we introduce strain as a tuning parameter to tailor the energy order of the bright, spin- and momentum-forbidden dark excitons in WSe2-ML, which enable us to even approximately infer the energy locations of the dark excitons with respect to that of the bright exciton.

Keywords: two-dimensional materials, transition-metal dichalcogenides, exciton fine structures, tight-binding model, Bethe-Salpeter equation