ANISOTROPIC EXCITON IN TWO-DIMENTIONAL BLACKPHOSPHORUS IN A UNIFORM MAGNETIC FIELD: AN ALGEBRA APPROACH
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Abstract
Exciton in monolayer semiconductor materials is of widespread interest due to their important applications in optoelectronics. An algebraic approach has been developed for excitons in monolayer transition-metal dichalcogenides with critical results. The present work extends this algebraic approach to excitons in another conductive material with an anisotropic structure: monolayer black phosphorus. This problem presents a more complex structure; however, we have developed an algebraic representation of the Schrödinger equation using quantum creation and annihilation operators. A basis set of wave functions was constructed, allowing us to derive analytical matrix elements related to these basis functions. By combining these results with algebraic calculations, we applied regulated perturbation theory in the presence of a magnetic field, achieving results consistent with other calculations, even at the zero-approximation order. These results are a critical step toward applying the algebraic method to anisotropic two-dimensional excitons in higher-approximation orders in future studies.
Keywords
algebraic method, anisotropy, annihilation and creation operators, exciton, monolayer black phosphorus, regulated perturbation theory
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References
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