The influence of disorder on the exciton spectra in two-dimensional structures

We study the joint effect of disorder and Coulomb interaction screening on the exciton spectra in two-dimensional (2D) structures. These can be van der Waals structures or heterostructures of organic (polymeric) semiconductors as well as inorganic substances like transition metal dichalcogenides. We consider 2D screened hydrogenic problem with Rytova - Keldysh interaction by means if so-called fractional Scrodinger equation. Our main finding is that above synergy between screening and disorder either destroys the exciton (strong screening) or promote the creation of a bound state, leading to its collapse in the extreme case. Our second finding is energy levels crossing, i.e. the degeneracy (with respect to index µ) of the exciton eigenenergies at certain discrete value of screening radius. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in above 2D semiconductor structures. Hence, they should be considered in device applications, where the in...本研究聚焦于二维（2D）结构中无序与库仑相互作用屏蔽效应对激子（exciton）能谱的联合影响。此类结构可涵盖有机（聚合）半导体的范德华结构或异质结，以及过渡金属硫族化合物（transition metal dichalcogenides）等无机材料体系。我们借助所谓的分数阶薛定谔（fractional Schrödinger）方程，研究采用里托娃-凯尔迪什（Rytova-Keldysh）相互作用的二维屏蔽类氢体系问题。本研究的核心发现为：上述屏蔽与无序间的协同效应，在强屏蔽条件下会消解激子，或是促进束缚态形成，极端情形下甚至会导致激子崩解。本研究的第二项发现为能级交叉现象：即当屏蔽半径取特定离散值时，激子本征能级关于指标μ发生简并。后述效应还可能与前述二维半导体结构中激子混沌行为的量子表征相关。因此，在涉及……的器件应用中，需将此类效应纳入考量。