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We derive an analytical expression for $s$-state exciton energies in monolayer transition-metal dichalcogenides (TMDCs): $E_{\text{ns}}=-{\text{Ry}}^*\times P_n/{(n-1/2+0.479\, r^*_0/\kappa)^2}$, $n=1,2,...$, where $r^*_0$ and $\kappa$ are the dimensionless screening length and dielectric constant of the surrounding medium; $\text{Ry}^*$ is an effective Rydberg energy scaled by the dielectric constant and exciton reduced mass; $P_n(r^*_0/\kappa)$ is a function of variables $n$ and $r^*_0/\kappa$. Its values are around 1.0 so we consider it a term that corrects the Rydberg energy. Despite the simple form, the suggested formula gives exciton energies with high precision compared to the exact numerical solutions that accurately describe recent experimental data for a large class of TMDC materials, including WSe$_2$, WS$_2$, MoSe$_2$, MoS$_2$, and MoTe$_2$. To achieve these results, we have developed a so-called regulated perturbation theory by combining the conventional perturbation method with several elements of the Feranchuk-Komarov operator method, including the Levi-Civita transformation, the algebraic calculation technique via the annihilation and creation operators, and the introduction of a free parameter to optimize the convergence rate of the perturbation series. This universal form of exciton energies could be helpful in various physical analyses, including retrieval of the material parameters such as reduced exciton mass and screening length from the available measured exciton energies., Comment: 5 pages, 1 figure, 3 tables, 1 supplementary

Reduced exciton mass, polarizability, and dielectric constant of the surrounding medium are essential properties for semiconducting materials, and they have been extracted recently from the magnetoexciton energies. However, the acceptable accuracy of the suggested method requires very high magnetic intensity. Therefore, in the present paper, we propose an alternative method of extracting these material properties from recently available experimental magnetoexciton s-state energies in monolayer transition-metal dichalcogenides (TMDCs). The method is based on the high sensitivity of exciton energies to the material parameters in the Rytova-Keldysh model. It allows us to vary the considered material parameters to get the best fit of the theoretical calculation to the experimental exciton energies for the $1s$, $2s$, and $3s$ states. This procedure gives values of the exciton reduced mass and $2D$ polarizability. Then, the experimental magnetoexciton spectra compared to the theoretical calculation also determine the average dielectric constant. Concrete applications are presented only for monolayers WSe$_2$ and WS$_2$ from the recently available experimental data; however, the presented approach is universal and can be applied to other monolayer TMDCs. The mentioned fitting procedure requires a fast and effective method of solving the Schr\"{o}dinger equation of an exciton in monolayer TMDCs with a magnetic field. Therefore, we also develop such a method in this paper for highly accurate magnetoexciton energies., Comment: 10 pages, 5 figures, 4 tables; submitted to Phys. Rev. B

It is widely comprehended that temperature may cause phonon-exciton scattering, enhancing the energy level's linewidth and leading to some spectrum shifts. However, in the present paper, we suggest a different mechanism that allows the thermal motion of the exciton's center of mass (c.m.) to affect the magnetoexciton energies in monolayer dichalcogenides (TMDCs). By the nontrivial but precise separation of the c.m. motion from an exciton in a monolayer TMDC with a magnetic field, we obtain an equation for the relative motion containing a motional Stark term proportional to the c.m. pseudomomentum, related to the temperature of the exciton gas but neglected in the previous studies. Solving the Schr\"odinger equation without omitting the motional Stark potential at room temperature shows approximately a few meV thermal-magnetic shifts in the exciton energies, significant enough for experimental detection. Moreover, this thermal effect causes a change in exciton radius and diamagnetic coefficient and enhances the exciton lifetime as a consequence. Surprisingly, the thermoinduced motional Stark potential breaks the system's SO(2) symmetry, conducting new peaks in the exciton absorption spectra at room temperature besides those of the $s$ states. This mechanism could be extended for other magnetoquasiparticles such as trions and biexcitons., Comment: 8 pages, 4 figures, 3 tables for main manuscript; 20 pages, 6 figures, 6 tables for supplementary. Published on Physical Review B