We present a theory that studies the state composition of a bound exciton in magnetic field. Using a basis set made of products of free electron and hole wave functions in Landau gauge, we derive a secular equation which shows the relation between Landau levels (LLs) of the electron and hole when a bound exciton is formed. Focusing on excitons in the light cone, we establish a scattering selection rule for the interaction of an electron in LL $n_{\text{e}}$ with a hole in LL $n_{\text{h}}$. We solve the resulting secular equation and identify a simple pairing law, $n_{\text{e}}=n_{\text{h}}+l$, which informs us on the construction of a bound exciton state with magnetic quantum number $l$, and on the interaction of the exciton magnetic moment with magnetic field. We obtain good agreement between theory results and recent measurements of the diamagnetic shifts of exciton states in ${\mathrm{WSe}}_2$ monolayers.

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• Excitons
• Landau levels
• Magneto-optics
• 2-dimensional systems
• Transition metal trichalcogenides
• Numerical techniques