Programme

P.41 -- Poster, VCTP-46

Date: Wednesday, 6 October 2021

Time: 08:30 - 10:00

Temperature effect on exciton energy spectra of transition-metal dichalcogenides monolayers

\textbf{Duy-Nhat Ly} (1), Thanh-Truc N. Huynh (2), Ngoc-Hưng Phan (1) and Van-Hoang Le (1)

(1) Ho Chi Minh City University of Education, Dist. 5, HCMC; (2) Marie Curie High School, Dist. 3, HCMC

Energy spectra of an exciton in transition metal dichalcogenide monolayers (TMDs) have been measured in the laboratory at temperatures below 300 K, where the temperature effect is still essential. This effect has been explained mainly based on exciton-phonon interactions, but there is still a large difference between the experiments and the theoretical estimation [1]. This report presents a new mechanism where the temperature can affect exciton energy due to the magnetic field. Considering the two-dimensional exciton in the magnetic field perpendicular to the plane the Hamiltonian has the form \[\hat H = \frac{1}{{2m}}{\hat p^2} + \frac{{{e^2}{B^2}}}{{8m}}({x^2} + {y^2}) + {V_{h - e}}(r) + \frac{{\alpha \,eB}}{2}\;{\hat l_z} - \frac{1}{M}\left( {e\vec B \times {{\vec P}_0}} \right).\,\vec r + \frac{1}{{2M}}{P_0}^2,\] where we use the notations: the effective masses of the electron and hole $m_e$, $m_h$, the exciton reduced mass $m = {m_e}{m_h}/({m_e} + {m_h})$, $M = {m_e} + {m_h}$, $\alpha = ({m_h} - {m_e})/{m_h}{m_e}$. Here, the quasimomentum ${\vec P_0}$ of the exciton center of mass is an eigenvalue of the operator ${\hat P_0} = \hat P - e\vec B \times \vec r/2$ with the momentum operator of the center of mass $\hat P$. This quantity is conserved for the considered system. ${V_{h - e}}(r)$ is the electron-hole interaction described by the Keldysh potential for the exciton in TMD monolayers. The above Hamiltonian was obtained through a non-trivial process of separating the center of mass from the electron-hole system [2]. In recent works, ${\hat P_0}$ is neglected, and only s-states are considered when angular momentum is equal to zero, ${\hat l_z} = 0$. However, if we consider excitons as a thermally interacting system, the terms containing ${\hat P_0}$ in the Hamiltonian somehow contribute to the exciton energy and can not be neglected. Here, the relation to temperature is given by ${P_0}^2 = 2M\,{k_B}T$ with the Boltzmann constant ${k_B}$. The temperature-related component of the Hamiltonian has a potential-barrier form, similar to the electric field in the Stark effect, so that the exciton energy will have an imaginary part related to the tunneling probability. Therefore, when calculating the exciton energy spectra, it is possible to calculate the lifetime part contributed by temperature through a new mechanism via the magnetic field. We qualitatively investigate the mentioned effect showing that the thermal motion of the center of mass enhanced by the external magnetic field affects the exciton energy spectra and their level width—the greater the temperature, the bigger the tunneling effect. It can be explained through the bending of the effective potential by the quasimomentum via the magnetic field. Also, the predicted effect is supported by the lasted experiments showing that the width of the spectrum increases with higher values of the magnetic field. Quantitative research will be continued by numerically solving the Schrödinger equation. \noindent [1] A. Arora, et al., Excited-state trions in monolayer WS2, Phys.Rev.Lett. 123 (2019) 167401. \noindent [2] Duy-Nhat Ly, Ngoc-Tram D. Hoang, and Van-Hoang Le, Comment on “Excitons, trions, and biexcitons in transition-metal dichalcogenides: Magnetic-field dependence,”Phys.Rev.B 101 (2020) 127401.

Presenter: Ly Duy-Nhat