Binding energies of exciton complexes in transition metal dichalcogenide monolayers and effect of dielectric environment

Abstract

Excitons, trions, biexcitons, and exciton-trion complexes in two-dimensional transition metal dichalcogenide sheets of MoS2, MoSe2, MoTe2, WS2 and WSe2 are studied by means of density functional theory and path integral Monte Carlo method in order to accurately account for the particle-particle correlations. In addition, the effect of dielectric environment on the properties of these exciton complexes is studied by modifying the effective interaction potential between particles. Calculated exciton and trion binding energies are consistent with previous experimental and computational studies, and larger systems such as biexciton and exciton-trion complex are found highly stable. Binding energies of biexcitons are similar or higher than those of trions, but the binding energy of the trion depends significantly stronger on the dielectric environment than that of biexciton. Therefore, as a function of an increasing dielectric constant of the environment the exciton-trion complex "dissociates" to a biexciton rather than to an exciton and a trion.Layered transition metal dichalcogenides (TMD) are chemically, thermally, and mechanically stable even in the monolayer form, and thus, provide an ideal platform for studying condensed matter physics in two dimensions. The semiconducting TMDs present many unusual optical properties such as strong excitonic effects 1 , valley-dependent circular dichroism 2 , and second-harmonic generation 3 , whose magnitude depends sensitively on the number of layers. For instance, the prototypical MoS 2 material is a semiconductor with 1.1 eV indirect band gap in bulk, but 1.9 eV direct band gap in the monolayer 1 . Importantly, the reduced dimensionality is manifested in a large exciton binding energy of 0.5-1 eV, but also of significant binding energy in the case of charged excitons, or trions, consisting of three charge carriers. This suggests that even larger complexes might be stable. Indeed, first experimental reports assigned to biexciton formation have very recently appeared in the literature [4][5][6] . Theoretical studies are invaluable in predicting the stability of these complexes and in interpreting the experimental results. Excitons can be calculated reliably from firstprinciples by solving the Bethe-Salpeter equation (BSE) on top of quasi-particle band structure. Binding energies have also been calculated using simple variational or tight-binding models based on an effective 2D interaction potential and the effective mass approach 6-13 , yielding fairly good agreement with experiments and with the BSE results in the case of excitons. This has also raised interest to apply similar approaches to study larger exciton complexes 6,14 , in comparison to the theoretical estimates based on quantum well systems 4,15,16 . Difficulties in constructing reasonable wave function ansatz in the case of the larger complexes hinders straightforward extension of the simple variational models. Within the effective mass approach, quantum Monte Carlo (QMC) methods, such as diffusion Monte Carlo and...

Magnetooptics of Exciton Rydberg States in a Monolayer Semiconductor

“…1. (Here we use m r =0.20m 0 , which is slightly larger than predicted by theory [19,21]; however this value is consistent with modeling of σ 1s [40] and as shown below is independently recommended by the high-field shifts of the 3s/4s states.) In marked contrast to the 1s state, the quadratic shift of the 2s state is ∼15× larger (σ 2s = 4.6 ± 0.2 µeV/T 2 ), confirming that the 2s exciton has a considerably larger radius r 2s √ 15 r 1s 6.6 nm.…”

“…The very different energy shifts of the 2s, 3s, and 4s excited states of X 0 are observed and studied for the first time. This permits not only their unambiguous identification but also allows for direct quantitative comparison with leading theoretical models based on the non-hydrogenic screened Keldysh potential [19][20][21]. A value of m r is experimentally obtained.…”

“…have been reported based on various linear and nonlinear optical spectroscopies [10][11][12][13][14][15][16]. Correct identification and quantitative measurements of excited excitons are of critical importance in this field, because they provide direct insight into the non-hydrogenic attractive potential between electrons and holes that is believed to exist in 2D materials due to dielectric confinement and nonlocal screening [17][18][19][20][21]. This potential leads, for example, to an unconventionally-spaced Rydberg series of excited excitons and can generate an anomalous ordering of (s, p, d ) levels [10].…”

“…This potential leads, for example, to an unconventionally-spaced Rydberg series of excited excitons and can generate an anomalous ordering of (s, p, d ) levels [10]. Crucially, these excited states allow one to directly estimate the free-particle bandgap and binding energy of the X 0 ground state [10][11][12][13][14][15], both key material parameters that are otherwise difficult to measure in monolayer TMDs, and which are necessarily very sensitive to the surrounding dielectric environment [14,21,22,24]. Greatly desired, therefore, are incisive experimental tools for detailed studies of excited excitons in 2D semiconductors.…”

Observation of Intervalley Biexcitonic Optical Stark Effect in Monolayer WS2

“…Recent research has revealed significant interactions between individual excitons in monolayer TMDs. In particular, two excitons at different valleys can be bound to form an excitonic molecule, the intervalley biexciton, with unusually large binding energies (40−70 meV) [9,10,[26][27][28]. These intervalley biexcitons offer an effective channel to couple the two valleys, with selection rules different from those for single excitons.…”