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arXiv 2407.01477cond-mat.mtrl-sci
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单层过渡金属二硫族化物中的激子能量解析表达式

Analytical exciton energies in monolayer transition-metal dichalcogenides

Hanh T. Dinh, Ngoc-Hung Phan, Duy-Nhat Ly, Dai-Nam Le, Ngoc-Tram D. Hoang, Nhat-Quang Nguyen, Phuoc-Thien Doan, Van-Hoang Le

AI总结:

本文推导了单层过渡金属二硫族化物中$s$态激子能量的高精度解析表达式,并基于正则化微扰理论,利用该公式从实验数据中准确提取激子约化质量和屏蔽长度等材料参数。

摘要:

我们推导了单层过渡金属二硫族化物(TMDCs)中$s$态激子能量的解析表达式:$E_{\ ext{ns}}=-{\ ext{Ry}}^*\ imes P_n/{(n-1/2+0.479\, r^*_0/κ)^2}$,$n=1,2,...$,其中$r^*_0$和$κ$分别是周围介质的无量纲屏蔽长度和介电常数;$\ ext{Ry}^*$是由介电常数和激子约化质量标度的有效里德伯能量;$P_n(r^*_0/κ)$是变量$n$和$r^*_0/κ$的函数。其值约为1.0,因此我们将其视为修正里德伯能量的项。尽管形式简单,与准确描述包括WSe$_2$、WS$_2$、MoSe$_2$、MoS$_2$和MoTe$_2$在内的一大类TMDC材料近期实验数据的精确数值解相比,所提出的公式仍给出了高精度的激子能量。为了获得这些结果,我们通过将常规微扰方法与Feranchuk-Komarov算子方法的几个要素相结合,开发了一种所谓的正则化微扰理论,包括Levi-Civita变换、通过产生和湮灭算子进行的代数计算技术,以及引入自由参数以优化微扰级数的收敛速率。这种激子能量的普适形式可能有助于各种物理分析,包括从可用的测量激子能量中提取材料参数,如激子约化质量和屏蔽长度。

英文摘要:

We derive an analytical expression for $s$-state exciton energies in monolayer transition-metal dichalcogenides (TMDCs): $E_{\text{ns}}=-{\text{Ry}}^*\times P_n/{(n-1/2+0.479\, r^*_0/κ)^2}$, $n=1,2,...$, where $r^*_0$ and $κ$ 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; $P_n(r^*_0/κ)$ is a function of variables $n$ and $r^*_0/κ$. 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.

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