NGHIÊN CỨU EXCITON TRUNG HÒA TRONG ĐƠN LỚP DICHALCOGENIDE KIM LOẠI-CHUYỂN TIẾP ĐẶT TRONG TỪ TRƯỜNG ĐỀU BẰNG PHƯƠNG PHÁP TOÁN TỬ

Abstract

This study proposes an effective method to solve the Schrödinger equation for the neutral exciton problem in a homogeneous magnetic field by combining the traditional FK (Feranchuk-Komarov) operator method with the direct Fourier transform in space (x, y). The proposed framework is well suited to experimental designs and provides a foundation for extending the analysis to two-electron atomic systems, such as the trion problem in monolayer transition metal dichalcogenides (TMDs). We obtained zero-order analytic energy in a homogeneous magnetic field of any intensity, achieving a deviation of less than 0.6% compared to other studies. Additionally, we calculated the numerical energy with an accuracy of 10^-6, and the results are consistent with other works, showing an average deviation of 0.03% when the wave function is expanded to 30 terms. Furthermore, we developed a calculation program in FORTRAN, utilizing MPI (Message Passing Interface) parallel programming to calculate matrix elements and solve eigenvalue equations. This advancement improves computational times for the one-electron atom problem and paves the way for solving more complex problems, such as the trion problem.