Jahan K Luhluh, Boda A, Shankar I V, Raju Ch Narasimha, Chatterjee Ashok
School of Physics, University of Hyderabad, Hyderabad, 500046, Telangana, India.
Sci Rep. 2018 Mar 22;8(1):5073. doi: 10.1038/s41598-018-23348-9.
The problem of an exciton trapped in a Gaussian quantum dot (QD) of GaAs is studied in both two and three dimensions in the presence of an external magnetic field using the Ritz variational method, the 1/N expansion method and the shifted 1/N expansion method. The ground state energy and the binding energy of the exciton are obtained as a function of the quantum dot size, confinement strength and the magnetic field and compared with those available in the literature. While the variational method gives the upper bound to the ground state energy, the 1/N expansion method gives the lower bound. The results obtained from the shifted 1/N expansion method are shown to match very well with those obtained from the exact diagonalization technique. The variation of the exciton size and the oscillator strength of the exciton are also studied as a function of the size of the quantum dot. The excited states of the exciton are computed using the shifted 1/N expansion method and it is suggested that a given number of stable excitonic bound states can be realized in a quantum dot by tuning the quantum dot parameters. This can open up the possibility of having quantum dot lasers using excitonic states.
利用里兹变分法、1/N展开法和移位1/N展开法，研究了存在外磁场时，二维和三维砷化镓高斯量子点（QD）中捕获的激子问题。得到了激子的基态能量和结合能作为量子点尺寸、限制强度和磁场的函数，并与文献中的结果进行了比较。变分法给出了基态能量的上限，而1/N展开法给出了下限。结果表明，移位1/N展开法得到的结果与精确对角化技术得到的结果非常吻合。还研究了激子尺寸和激子振子强度随量子点尺寸的变化。利用移位1/N展开法计算了激子的激发态，并提出通过调整量子点参数，可以在量子点中实现一定数量的稳定激子束缚态。这为利用激子态制造量子点激光器开辟了可能性。
