Landau-level composition of bound exciton states in magnetic field

TL;DR

This paper develops a theoretical framework to analyze the composition of bound exciton states in magnetic fields, revealing a pairing law between Landau levels and matching experimental diamagnetic shift data.

Contribution

It introduces a secular equation based on Landau gauge wavefunctions that uncovers a simple pairing law for Landau levels in bound excitons, advancing understanding of exciton magnetic properties.

Findings

Derived a secular equation relating electron and hole Landau levels.

Established a pairing law $n_e = n_h + l$ for exciton states.

Achieved good agreement with experimental diamagnetic shift measurements.

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.