Retrieval of fundamental material parameters of monolayer transition metal dichalcogenides from experimental exciton energies: An analytical approach

Abstract

We propose a straightforward and highly accurate method for extracting material parameters such as screening length, bandgap energy, exciton reduced mass, and the dielectric constant of the surrounding medium from experimental magnetoexciton energies available for monolayer transition metal dichalcogenides (TMDCs). Our approach relies on analytical formulations that allow us to calculate the screening length $r_0$ and bandgap energy $E_g$ directly from the experimental $s$-state exciton energies $E_{1s}$, $E_{2s}$, and $E_{3s}$. We also establish a relationship between the surrounding dielectric constant $\kappa$ and the exciton reduced mass $\mu$. This relationship simplifies the Schr{\"o}dinger equation for a magnetoexciton in a TMDC monolayer, transforming it into a one-parameter equation that depends solely on the single material parameter $\mu$. Furthermore, we develop an analytical formula with high accuracy for magnetoexciton energies as a function of the exciton reduced mass: $E(B,\mu)$. Then, the inverse of this formula allows us to calculate the exciton reduced mass from experimental data on magnetoexciton energies. By applying this method, we extract key material parameters, $E_g$, $r_0$, $\mu$, and $\kappa$, from the magnetoexciton energies of monolayer TMDCs, including WSe$_2$, WS$_2$, MoSe$_2$, and MoS$_2$, encapsulated by hexagonal boron nitride (hBN) slabs in various current experiments. The material properties we retrieve complement and correct existing experimental and theoretical data. Additionally, we develop an analytical method for calculating diamagnetic coefficients and exciton radii with high accuracy compared to numerical calculations. Based on this method, we provide diamagnetic coefficients and exciton radii computed using the extracted material parameters.