TEMPERATURE EFFECT ON LOW ENERGY LEVEL OF NEUTRAL EXCITON IN A UNIFORM MAGNETIC FIELD
Main Article Content
Abstract
This article presents the temperature effect on the neutral exciton energy spectrum in the WSe2 monolayer in the magnetic field by a new mechanism that was first investigated in this work. This mechanism is entirely different from the exciton-phonon mechanism studied by many previous works in the absence of magnetic fields. By separating the center of the mass movement for the neutral exciton and obtaining the correct Hamiltonian, we found a term related to temperature and magnetic fields that were ignored in previous studies. We numerically solved the Schrodinger equations using the Feranchuk-Komarov operator method for the 1s, 2s, and 3s states and investigated the effect of temperature on the energy spectrum. The results show that with a magnetic field of up to 100 Tesla, the exciton's energy at the 3s state at 300K can be nearly 6% different from that at 0K. We also calculated the exciton radius and found that it varies with temperature. For example, with a 100 Tesla magnetic field, the radius at 300K increased by more than 50% compared to at 0K. This result suggests that we have to investigate further the temperature effect on the physical properties of exciton in TMD monolayer.
Keywords
annihilation and creation operators, basic set, exciton, FK operator method, Keldysh potential, two-dimensional atomic systems
Article Details
References
Arora, A., Koperski, M., Nogajewski, K., Marcus, J., Faugeras, C., & Potemski, M. (2015). Excitonic resonances in thin films of WSe 2 : from monolayer to bulk material. Nanoscale, 7(23), 10421.
Cao, T.-X. H., Ly, D.-N., Hoang, N.-T. D., & Le, V. H. (2019). High-accuracy numerical calculations of the bound states of a hydrogen atom in a constant magnetic field with arbitrary strength. Computer Physics Communications, 240, 138.
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.
Cudazzo, P., Tokatly, I. V, & Rubio, A. (2011). Dielectric screening in two-dimensional insulators: Implications for excitonic and impurity states in graphane. Physical Review B, 84(8), 085406.
Feranchuk, I., Ivanov, A., Le, V. H., & Ulyanenkov, A. (2015). Non-perturbative Description of Quantum Systems (Vol. 894). Cham: Springer International Publishing.
He, K., Kumar, N., Zhao, L., Wang, Z., Mak, K. F., Zhao, H., & Shan, J. (2014). Tightly bound excitons in monolayer WSe2. Physical Review Letters, 113(2), 1.
Hoang, D. 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, 31-37.
Hoang, N. T. D., Nguyen, D. A. P., Hoang, V. H., & Le, V. H. (2016). Highly accurate analytical energy of a two-dimensional exciton in a constant magnetic field. Physica B: Condensed Matter, 495, 16-20.
Hoang, N. D., Ly, D. N., & Le, V. H. (2020). Comment on “Excitons, trions, and biexcitons in transition-metal dichalcogenides: Magnetic-field dependence.” Physical Review B, 101(12), 127401.
Keldysh, L. V. (1979). Coulomb interaction in thin semiconductor and semimetal films. JETP Lett., 29(11), 658-660. Retrieved from jetpletters.ac.ru/ps/1458/article_22207.shtml
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.
Ly, D. N., Hoang, N. D., & Le, V. H. (2021). Highly accurate energies of a plasma-embedded hydrogen atom in a uniform magnetic field. Physics of Plasmas, 28(6), 063301.
Netlib.org. LAPACK: Linear Algebra PACKage. (n.d.). Subroutine DSYGVX.f. Retrieved from http://www.netlib.org/lapack/explore-ht-ml/d2/d97/dsyevx-8f.html
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, 152-164.
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.