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Effect of electron-electron interactions on optical properties of GaN/AIN quantum wells: a nonlinear Schroedinger equation approach

机译：电子-电子相互作用对GaN / AIN量子阱的光学性质的影响：非线性Schroedinger方程方法

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Researchers usually neglect the electron-electron interaction effect when they study the optical properties of semiconducting nanostructures through the compact density matrix approach. In the existing papers, this work has also been done through self-consistent solution of the Schrodinger and Poisson equations. For the first time, we have investigated the electronic and optical properties of wurtzite GaN/AlN quantum wells in the presence of electron-electron interactions assuming weak electron-electron scattering through a numerical solution of a nonlinear Schrodinger equation. It is shown that the electron-electron interaction effect leads to the removal of the N-fold degeneracy in the energy levels of N-well multiple quantum well systems. Effects of different parameters such as electric field, the strength of the electron-electron interaction, a total length of the system and also two different numbers of wells (1 and 2) on the mentioned optical properties have been investigated. Also, we observed redshifts in the optical rectification coefficient peak positions when the nonlinear parameter increased. Finite difference self-consistent method was employed to solve the nonlinear Schrodinger equation and we demonstrated the method convergence. Finally, we illustrated the accuracy of the method by comparing our energy values with those of the Sinc method.
机译：当研究人员通过紧凑密度矩阵方法研究半导体纳米结构的光学特性时，他们通常会忽略电子与电子的相互作用。在现有论文中，这项工作还通过Schrodinger和Poisson方程的自洽解来完成。首次，我们通过非线性Schrodinger方程的数值解，假设存在弱电子-电子散射，研究了存在电子-电子相互作用的纤锌矿GaN / AlN量子阱的电子和光学性质。结果表明，电子-电子相互作用效应导致N阱多量子阱系统能级的N倍简并性的消除。研究了不同参数（例如电场，电子-电子相互作用的强度，系统的总长度以及两个不同数量的阱（1和2））对上述光学性能的影响。此外，当非线性参数增加时，我们观察到了光学整流系数峰值位置的红移。采用有限差分自洽方法求解非线性薛定inger方程，并证明了方法的收敛性。最后，我们通过将能量值与Sinc方法的能量值进行比较来说明该方法的准确性。

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