Stephanovich V A, Kirichenko E V, Książek K, Sauco Jackie Harjani, Brito Belén López
Institute of Physics, <a href="https://ror.org/04gbpnx96">University of Opole</a>, Oleska 48, 45-052, Opole, Poland.
Department of Mathematics, <a href="https://ror.org/01teme464">Universidad de Las Palmas de Gran Canaria</a>, Campus de Tafira Baja, Las Palmas C.P. 35017, Spain.
Phys Rev E. 2024 Aug;110(2-1):024201. doi: 10.1103/PhysRevE.110.024201.
We study the synergy between disorder (phenomenologically modeled by the introduction of Riesz fractional derivative in the corresponding Schrödinger equation) and spin-orbit coupling (SOC) on the exciton spectra in two-dimensional (2D) semiconductor structures. We demonstrate that the joint impact of "fractionality" and SOC considerably modifies the spectrum of corresponding "ordinary" (i.e., without fractional derivatives) hydrogenic problem, leading to the non-Poissonian statistics of the adjacent level distance distribution. The latter fact is strong evidence of the possible emergence of quantum chaotic features in the system. Using analytical and numerical arguments, we discuss the possibilities to control the above chaotic features using the synergy of SOC, Coulomb interaction, and "fractionality," characterized by the Lévy index μ.
我们研究了无序（通过在相应的薛定谔方程中引入里斯分数导数进行唯象建模）与自旋轨道耦合（SOC）在二维（2D）半导体结构中的激子光谱上的协同作用。我们证明，“分数性”和SOC的联合影响极大地改变了相应“普通”（即无分数导数）类氢问题的光谱，导致相邻能级间距分布呈现非泊松统计。后一事实有力地证明了系统中可能出现量子混沌特征。通过解析和数值论证，我们讨论了利用SOC、库仑相互作用和以 Lévy 指数μ表征的“分数性”的协同作用来控制上述混沌特征的可能性。
