Transition-metal dichalcogenide (TMD)-based atomically thin semiconductors are materials with strongly bound excitonic complexes leading to an optical response. The present article discusses the origin of excitons and highlights the theory of excitons in two-dimensional (2D) semiconductors, focusing on TMD-based atomically thin semiconductors.
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What are Excitons?
Coulombic attraction between a negatively charged electron and a positively charged hole form excitons. The photoexcitation in semiconductors exhibits a spectrally narrow linewidth resulting in exciton formation. The excitons containing large oscillator strength and enhanced light-matter interaction allow efficient recombination and emission of light.
The nature of an exciton is like an atom in a crystal lattice with its inherent internal fine structure. Although excitons have great significance in physics, their practical application remains unexplored. Bound exciton states dictate the optical properties of 2D materials such as TMDs. Excitons have strong Coulomb interaction in low dimensions and reduced dielectric screening compared to bulk crystals.
TMD-Based Atomically Thin Semiconductors
A TMD-based single-layered plane built from three atoms in the form of X-M-X has a trigonal, hexagonal, or rhombohedral polymorphic structure. Due to the promising optoelectronic properties, the semiconducting TMDs have received considerable attention from researchers.
The properties of monolayered crystals depend on the chemical composition, structural phase, and substrate. Hence, after TMD exfoliation, it is critical to place them on a properly prepared SiO2/Si substrate, to improve the contrast in optical microscopy.
Molybdenum disulfide (MoS2) thinned down to a single layer exhibited better photoluminescence (PL) than multilayered crystals. A similar trend was observed in MoS2, molybdenum diselenide (MoSe2), molybdenum ditelluride (MoTe2), tungsten disulfide (WS2), and tungsten diselenide (WSe2) semiconductors. These TMDs had varying magnitudes of differences between samples and with different numbers of layers.
Comparison of PL peak energy position to the known spectral positions of the excitonic transitions in bulk MoS2 confirmed strong PL dominated by an excitonic (X) transition. The exciton generation in each valley couple circularly polarized light with excitation in each valley. The exciton series consists of bright s-series, which can be probed by PL dynamics, different emission configurations, the different temperature dependence of emissions, or by using a tilted magnetic field. Additionally, the exciton series also has two types of dark states-spin-forbidden and excited excitons states, probed using two-photon spectroscopy.
In addition to strongly bound excitons, TMDs exhibit another type of bound complexes in their photoresponse, namely trions. These trion complexes consist of three particles, i.e., two electrons and one hole (X-) or two holes and one electron (X+) for negatively and positively charged types, respectively.
With the complicated numerical and conceptual challenges of density functional theory (DFT), Bethe–Salpeter equation (BSE) theory, and the approximate nature of the simplified tight-binding methodology, one may turn to the latter, offering an optimal trade-off between numerical tractability and the ability to capture essential physical ingredients in the excitonic problem. This study allowed the tracking of exciton fine-structure evolution dependence on electron doping, the exchange interaction, and magnetic and electric fields.
In an article published in the journal Physical Review, the researchers derived an effective low-energy model for Bose-Fermi mixtures. They developed an exact diagonalization approach based on a discrete variable representation that predicts scattering and bound-state properties of the three charges in 2D TMDs.
Based on the solution of the quantum mechanical three-body problem, they could obtain the bound state energies of excitons and trions within an effective mass model, which follows quantum Monte Carlo predictions. Moreover, the diagonalization approach also gave access to excited states of the three-body system, which allowed the team to predict the scattering phase shifts of electrons and excitons that serve as input for a low-energy theory of interacting mixtures of excitons and charge carriers at finite density.
In another article recently published in the journal Nature Communications, researchers used a scattering-type scanning near-field optical microscope (s-SNOM) and acquired exciton spectra in atomically thin TMD microcrystals. To this end, the nano-optical data obtained revealed the material- and stacking-dependent exciton spectra of MoSe2, WSe2, and their heterostructures. Furthermore, the s-SNOM hyperspectral images uncovered how the dielectric screening modifies excitons at length scales as short as a few nanometers.
In conclusion, the 2D material-based excitons allow the researchers to explore the emerging physics and enable a broad range of photonic applications of these materials.
An ab initio-based tight-binding model can capture all the critical features of the electronic structures of TMDs. Furthermore, through the theory of excitons, the physics behind the excitonic spectrum in both mono- and bi-layer heterostructures can be understood. Band nesting can positively affect the fine structure of exciton, its Coulomb interactions, the topology of wave functions, screening, and the dielectric environment.
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References and Further Reading
Fey, C., Schmelcher, P., Imamoglu, A., & Schmidt, R. (2020). Theory of exciton-electron scattering in atomically thin semiconductors. Physical Review B, 101(19), 195417. https://journals.aps.org/prb/abstract/10.1103/PhysRevB.101.195417
Zhang, S., Li, B., Chen, X., Ruta, F. L., Shao, Y., Sternbach, A. J., ... & Basov, D. N. (2022). Nano-spectroscopy of excitons in atomically thin transition metal dichalcogenides. Nature Communications, 13(1), 1-8. https://www.nature.com/articles/s41467-022-28117-x
Bieniek, M., Sadecka, K., Szulakowska, L., & Hawrylak, P. (2022). Theory of Excitons in Atomically Thin Semiconductors: Tight-Binding Approach. Nanomaterials, 12(9), 1582. https://www.mdpi.com/2079-4991/12/9/1582
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