Exciton Spectra & Quantum Bandgaps, Screening Via Analytical Inversion

Researchers have developed a method to determine key material properties of two-dimensional semiconductors by analyzing exciton spectra. Duy-Nhat Ly, Thanh-Son Nguyen, Ngoc-Tram D. Hoang, and Van-Hoang Le of Ho Chi Minh City University of Education created an analytical procedure based on a solvable modified Kratzer model to retrieve parameters from monolayer transition-metal dichalcogenides. The work determines quasiparticle bandgaps, effective screening parameters, and energy scaling factors directly from the experimentally measured energies of the three lowest excitonic states. Once these parameters are known, the framework analytically predicts diamagnetic coefficients, exciton radii, and complete magnetoexciton spectra without introducing additional fitting parameters or matrix diagonalization. The team applied the method to WSe₂, WS₂, MoS₂, MoSe₂, and MoTe₂ monolayers, finding retrieved parameters aligned with independent experimental measurements and prior calculations.

The retrieval procedure consists of two complementary stages. In the first stage, explicit formulas determine the quasiparticle bandgap, effective screening parameter, and energy scaling factor directly from the experimentally measured energies of the three lowest excitonic states, from which the screening length is subsequently obtained. In the second stage, an analytical expression for the magnetic-field dependence of the exciton energies independently yields the reduced exciton mass, from which the surrounding dielectric constant is then calculated.

The study of two-dimensional semiconductors, particularly transition-metal dichalcogenides, continues to refine material characterization techniques, moving beyond computationally intensive numerical fitting toward streamlined analytical methods. Researchers are now able to determine key material properties by leveraging the solvable modified Kratzer model, a theoretical framework that offers surprising efficiency. A two-stage analytical procedure forms the core of this advancement, and its predictive capability is a key strength.

Duy-Nhat Ly, Thanh-Son Nguyen, Ngoc-Tram D. Hoang, and Van-Hoang Le have developed an analytical procedure leveraging the energies of just the three lowest excitonic states to determine crucial material characteristics. This approach bypasses the need for iterative fitting, a common bottleneck in materials analysis, and offers a direct pathway to understanding a material’s behavior. The core of their advancement lies in a retrieval procedure that consists of two complementary stages, with the subsequent stage focusing on the reduced exciton mass derived from the material’s response to magnetic fields via an analytical magnetoexciton expression, ultimately revealing the dielectric constant of the surrounding environment. This analytical theory offers a computationally efficient and physically transparent alternative for characterizing these increasingly important two-dimensional semiconductors through excitonic spectroscopy.

The team’s work centers on a two-stage analytical procedure utilizing the “solvable modified Kratzer model.” Initially, they demonstrate that explicit inversion formulas determine the quasiparticle bandgap, effective screening parameter, and energy scaling factor directly from the experimentally measured energies of the three lowest excitonic states, from which the screening length is subsequently obtained. The proposed analytical theory offers an efficient, physically transparent alternative to conventional numerical fitting procedures, providing a practical tool for rapid characterization of two-dimensional semiconductors via excitonic spectroscopy.

Conventional methods for characterizing two-dimensional semiconductors often rely on computationally intensive numerical fitting to extract key material properties from spectroscopic data. The team’s approach centers on leveraging the “solvable modified Kratzer model” to analyze exciton spectra, revealing material characteristics with increased efficiency. The retrieval procedure consists of two complementary stages, and from these initial values, the screening length is then calculated. The power of this framework extends beyond parameter retrieval.

The established method for characterizing two-dimensional semiconductors relies heavily on the Rytova, Keldysh (RK) potential, often paired with computationally intensive numerical solutions to the excitonic Schrödinger equation. While successful, these approaches require iterative fitting of multiple parameters, obscuring the individual physical roles of each and demanding significant processing power. The analytical framework detailed in this work offers a distinct alternative, validated through direct comparison with existing RK calculations and independent experimental measurements. This contrasts with typical RK-based methods requiring more extensive spectral data for accurate fitting; the retrieved material parameters demonstrated good agreement with independent experimental measurements and previous Rytova, Keldysh calculations, validating the model’s predictive power.

The ability to accurately characterize materials embedded in varying dielectric environments, from hexagonal boron nitride to more complex substrates, positions this method as a powerful tool for materials scientists seeking rapid, physically transparent insights into the properties of two-dimensional semiconductors. The framework establishes a quantitative bridge between the analytically solvable modified Kratzer model and the microscopic RK description, offering a practical means of characterization via excitonic spectroscopy.