Landau-level composition of bound exciton states in magnetic field

Abstract

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 wavefunctions 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 WSe${}_2$ monolayers.

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• Energy shifts and broadening of excitonic resonances in electrostatically-doped semiconductors
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• Magnetoexcitons and Massive Dirac Fermions in Monolayers of Transition Metal Dichalcogenides in a High Magnetic Field