Title: Analytical exciton energies in monolayer transition-metal dichalcogenides Show Chinese title

Title: 单层过渡金属二硫属化合物中的解析激子能级

Abstract: 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. Show Chinese abstract

Abstract: 我们推导出单层过渡金属二硫属化物（TMDCs）中$s$态激子能量的解析表达式：$E_{\text{ns}}=-{\text{Ry}}^*\times P_n/{(n-1/2+0.479\, r^*_0/\kappa)^2}$，$n=1,2,...$，其中$r^*_0$和$\kappa$是周围介质的无量纲屏蔽长度和介电常数；$\text{Ry}^*$是一个由介电常数和激子约化质量缩放的有效里德伯能量；$P_n(r^*_0/\kappa)$是变量$n$和$r^*_0/\kappa$的函数。 它的值大约为1.0，因此我们认为它是一个修正里德伯能量的项。 尽管形式简单，但所提出的公式与准确描述一类大量TMDC材料（包括WSe$_2$，WS$_2$，MoSe$_2$，MoS$_2$，和MoTe$_2$）最新实验数据的精确数值解相比，给出了高精度的激子能量。 为了获得这些结果，我们通过将传统微扰方法与费兰丘克-科马罗夫算符方法的几个要素相结合，发展了一种所谓的受控微扰理论，包括莱维-奇维塔变换、通过湮灭和产生算符的代数计算技术，以及引入一个自由参数以优化微扰级数的收敛速度。 这种激子能量的通用形式在各种物理分析中可能有所帮助，包括从可用的测量激子能量中提取材料参数，如有效激子质量和屏蔽长度。