Orbital, spin and valley contributions to Zeeman splitting of excitonic resonances in MoSe$_2$, WSe$_2$ and WS$_2$ monolayers

TL;DR

This paper provides a detailed optical analysis of Zeeman effects in monolayer transition metal dichalcogenides, introducing a semi-phenomenological model that accounts for valley, spin, and orbital contributions to excitonic splitting.

Contribution

It proposes a simple model for magnetic field effects on electronic states in MoSe₂, WSe₂, and WS₂ monolayers, emphasizing the importance of valley contributions and explaining large g-factors in emission lines.

Findings

Valley, spin, and orbital terms are essential for describing Zeeman splitting.

The model accurately fits absorption spectra and magneto-luminescence data.

Large g-factors are explained by bound excitons and dark state brightening.

Abstract

We present a comprehensive optical study of the excitonic Zeeman effects in transition metal dichalcogenide monolayers, which are discussed comparatively for selected materials: MoSe$_2$, WSe$_2$ and WS$_2$. We introduce a simple semi-phenomenological description of the magnetic field evolution of individual electronic states in fundamental sub-bands by considering three additive components: valley, spin and orbital terms. We corroborate the validity of the proposed description by inspecting the Zeeman-like splitting of neutral and charged excitonic resonances in absorption-type spectra. The values of all three terms are estimated based on the experimental data, demonstrating the significance of the valley term for a consistent description of magnetic field evolution of optical resonances, particularly those corresponding to charged states. The established model is further exploited for discussion of magneto-luminescence data. We propose an interpretation of the observed large g-factor values of low energy emission lines, due to so-called bound/localized excitons in tungsten based compounds, based on the brightening mechanisms of dark excitonic states.