Institute of Physics, Opole University, Oleska 48, 45-052, Opole, Poland.
Phys Chem Chem Phys. 2019 Oct 9;21(39):21847-21855. doi: 10.1039/c9cp04111g.
We study the role of disorder in the exciton spectra in two-dimensional (2D) semiconductors. These can be heterostructures, thin films and multilayers (so-called van der Waals structures) of organometallic perovskites, transition metal dichalcogenides and other semiconductors for optoelectronic applications. We model the disorder by introduction of a fractional Laplacian (with Lévy index μ, defining the degree of disorder) to the Scrödinger equation with 2D Coulomb potential. Combining analytical and numerical methods, we observe that the exciton exists only for μ > 1, while the point μ = 1 (strongest disorder) corresponds to the exciton collapse. We show also that in the fractional (disordered, corresponding to 1 < μ < 2; μ = 2 corresponds to the ordered case) 2D hydrogenic problem, the orbital momentum degeneracy is lifted so that its energy starts to depend not only on principal quantum number n but also on orbital m. These features can have a profound influence on the lifetime of optically generated excitons in the above 2D semiconductor structures. They should be taken into account while designing the photovoltaic cells, nanolasers and optical spintronics devices, where 2D excitons play a significant role.
我们研究了二维（2D）半导体中无序对激子谱的作用。这些可以是二维半导体的异质结构、薄膜和多层（所谓的范德瓦尔斯结构），包括有机金属钙钛矿、过渡金属二卤化物和其他用于光电子应用的半导体。我们通过在二维库仑势的薛定谔方程中引入分数拉普拉斯算子（具有定义无序程度的勒维指数μ）来模拟无序。通过结合分析和数值方法，我们观察到只有在μ>1 时才存在激子，而μ=1 时（最强无序）对应于激子崩溃。我们还表明，在分数（无序，对应于 1<μ<2；μ=2 对应于有序情况）二维氢问题中，轨道角动量简并被解除，因此其能量不仅取决于主量子数 n，还取决于轨道 m。这些特征可能对上述二维半导体结构中光生成激子的寿命产生深远影响。在设计光伏电池、纳米激光器和光学自旋电子器件时，需要考虑这些因素，其中二维激子起着重要作用。
