Two-dimensional exciton energy spectra of monolayer transition metal dichalcogenides

Photoexcitation is the production of an excited state of a quantum system by photon absorption. Photoexcitation creates bound electron–hole pairs, namely, excitons, in a direct bandgap semiconductor. So far, strongly bound excitons have been predicted theoretically and also observed experimentally in monolayer transition metal dichalcogenides (TMDs). Formidable efforts in matters research have been launched owing to the fact that the two-dimensional (2D) excitons play a key role in strongly enhanced photoluminescence, photocurrent generation, and are also involved in the excitonic absorption and recombination of valley polarization. These slew of applications makes the knowledge of the exciton energy spectrum fundamental to the study of strong light–matter interactions in these 2D semiconductors. A review of published literature has shown that majority of the available calculations have focused on the exciton ground states of the monolayer TMDs and only a few theoretical studies have been carried out for strongly bound excitons and s exciton Rydberg series. Generally, there is a deficiency of calculations of exciton energy spectrum.

As a matter of fact, there has been no report on excited state calculation with the variational method for monolayer TMDs. Recently, researchers from the School of Physics at Jilin University, Professor Jian-Zhong Zhang and Mr. Jin-Zhong Ma reported the 2D exciton energy spectra of a TMD monolayer in various dielectric environments. Technically, they calculated exciton states numerically using the effective mass model for the excitonic Hamiltonian. Their work is currently published in Journal of Physics: Condensed Matter.

In brief, the exciton energy spectra of monolayer transition metal dichalcogenides in various dielectric environments were studied with an effective mass model using the Keldysh potential for the screened electron–hole interaction. Additionally, the two-dimensional excitons were calculated by solving a radial equation with a shooting method, using boundary conditions that were derived by applying the asymptotic properties of the Keldysh potential.

The authors reported that for any given main quantum number n, the exciton Bohr orbit shrunk as |m| became larger (m represented the orbital quantum number) resulting in increased strength of the electron–hole interaction and a decrease of the exciton energy. Further, the two physicists observed that both the exciton energy and its effective radius decreased linearly with |m|. Interestingly, the screened hydrogen model [Phys. Rev. Lett. 116, 056401 (2016)] was found to describe the non-hydrogenic exciton Rydberg series reasonably well, although it failed to account for the linear dependence of the exciton energy on the orbital quantum number.

Remarkably, the two physicists constructed analytical variational wave-functions with the 2D hydrogenic wave-functions for a number of strongly bound exciton states, and further applied them to study the Stark effects in monolayer TMDs, with an analytical expression derived for evaluating the redshift of the ground state energy.

In summary, the study evaluated the 2D exciton energy spectra of monolayer TMDs with an effective mass model using the Keldysh potential for the screened electron–hole interaction. Overall, the numerical solution of the radial equation combined with the variational method provides a simple and effective approach for the study of 2D excitons in monolayer TMDs.