REGULATED PERTURBATION THEORY FOR NEUTRAL EXCITON ENERGY IN A UNIFORM MAGNETIC FIELD
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Abstract
Two-dimensional excitons in magnetic fields is an important problem because of the latest achievements in the application of exciton energy spectroscopy to retrieve structural information of monolayer transition metal dichalcogenides (TMD). The Feranchuk-Komarov (FK) operator method has been successfully used to calculate the numerical energy spectra for this system. In this work, the perturbation theory with the regulation of free parameter is used to calculate the neutral exciton energy in a uniform magnetic field with Keldysh potential. We first discussed the perturbation theory with general formulas. Then, the convergence of the solution taking into account the higher-order correction was studied with magnetic fields up to 120 Tesla. Numerical calculations are presented for ground states, on the other hand, general expressions allow calculations for excited states. The results are accurate with an error of less than 1% facilitating the further study of the problem to have an explicit analytical solution.
Keywords
annihilation and creation operators, basic set, FK operator method, exciton, Keldysh potential, two-dimensional atomic systems
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References
Chernikov, A., Berkelbach, T. C., Hill, H. M., Rigosi, A., Li, Y., Aslan, O. B.,… Heinz, T. F. (2014). Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS2. Physical Review Letters, 113(7), 076802.
Feranchuk, I., Ivanov, A., Le, V. H., & Ulyanenkov, A. (2015). Non-perturbative Description of Quantum Systems (vol. 894). Cham: Springer International Publishing.
Frenkel, J. (1931). On the Transformation of light into Heat in Solids. I. Physical Review,
37(1), 17.
Goryca, M., Li, J., Stier, A. V., Taniguchi, T., Watanabe, K., Courtade, E.,… Crooker, S. A. (2019). Revealing exciton masses and dielectric properties of monolayer semiconductors with high magnetic fields. Nature Communications, 10(1), 4172.
Hoang-Do, N. T., Hoang, V. H., & Le, V. H. (2013). Analytical solutions of the Schrödinger equation for a two-dimensional exciton in magnetic field of arbitrary strength. Journal of Mathematical Physics, 54(5), 052105.
Hoang-Do, N.-T., Pham, D. L., & Le, V. H. (2013). Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength. Physica B: Condensed Matter, 423, 31.
Keldysh, L. V. (1979). Coulomb interaction in thin semiconductor and semimetal films. JETP Lett., 29(11), 658.
Kylänpää, I., & Komsa, H.-P. (2015). Binding energies of exciton complexes in transition metal dichalcogenide monolayers and effect of dielectric environment. Physical Review B, 92(20), 205418.
Levi-Civita, T. (1956). Opere Metematiche. Memorie e Note. Vol. II: 1901 – 1907. Bologna: Nicola Zanichelli Editore.
Liu, E., van Baren, J., Taniguchi, T., Watanabe, K., Chang, Y. C., & Lui, C. H. (2019). Magnetophotoluminescence of exciton Rydberg states in monolayer WSe2. Physical Review B, 99(20), 205420.
McDonnell, L. P., Viner, J. J. S., Rivera, P., Xu, X., & Smith, D. C. (2020). Observation of intravalley phonon scattering of 2s excitons in MoSe 2 and WSe 2 monolayers. 2D Materials, 7(4), 045008.
Nguyen, D. A. P., Ly, D. N., Le, D. N., Hoang, N. T. D., & Le, V. H. (2019). High-accuracy energy spectra of a two-dimensional exciton screened by reduced dimensionality with the presence of a constant magnetic field. Physica E: Low-Dimensional Systems and Nanostructures, 113, 152.
Raja, A., Chaves, A., Yu, J., Arefe, G., Hill, H. M., Rigosi, A. F.,… Chernikov, A. (2017). Coulomb engineering of the bandgap and excitons in two-dimensional materials. Nature Communications, 8(May), 1.
Rytova, N. S. (1967). The screened potential of a point charge in a thin film. Vestnik Moskovskogo Universiteta. Fizika, 22(3), 30-37.
Stier, A. V., Wilson, N. P., Velizhanin, K. A., Kono, J., Xu, X., & Crooker, S. A. (2018). Magnetooptics of Exciton Rydberg States in a Monolayer Semiconductor. Physical Review Letters, 120(5), 057405.
Wannier, G. H. (1937). The Structure of Electronic Excitation Levels in Insulating Crystals. Physical Review, 52(3), 191.