Magnetoexcitons and Massive Dirac Fermions in Monolayers of Transition Metal Dichalcogenides in a High Magnetic Field

Abstract

We present a theory of the emission spectrum of magnetoexcitons interacting with a $ν= 1$ quantum Hall state of massive Dirac fermions in monolayer transition metal dichalcogenides in high magnetic fields. Using an ab initio-parametrized massive Dirac fermion model including valley and spin degrees of freedom, combined with exact diagonalization techniques, we show that interband emission from the massive Dirac Fermion magnetoexciton interacting with $ν= 1$ state directly probes intra-conduction-band excitations of the $ν= 1$. Many-body interactions with the filled massive Dirac fermion $ν= 1$ level yield a strong renormalization of the emission spectrum, including fully polarized emission, a pronounced redshift, and broadening relative to neutral and charged excitons. The calculated spectra are consistent with recent experiments [1-3], establishing magneto-spectroscopy as a probe of finite carrier densities in massive Dirac systems.

Figures (4)

• Figure 1: Top: monolayer MoS$_2$ in a magnetic field, illustrating cyclotron motion. Bottom: LL spectra at $B=10$ T for $K$ and $K'$ valleys, showing three model stages: (i) no SOC, (ii) SOC only, (iii) full spin–valley coupling ($g_e=-2$, $g_h=-2.2$). Background lines: $B=0$ bands (grey: no SOC, red/blue: spin-split). Dashed lines: selected LL labeled by $n$. Vertical arrows ($\sigma^\pm$) indicate optically allowed interband transitions.
• Figure 2: Schematic of a neutral exciton (a) in valley $K'$ and (b) in valley $K$ interacting with the $\nu=1$ state at $B=10$ T. Black arrows in $n=0$LL denote the fully filled $\nu=1$ state; a model degeneracy of 5 is used.
• Figure 3: Excitonic spectra of (a) an interband exciton interacting with $\nu=1$ and (b) an intraband exciton (final emission state), displayed on a common energy scale; colours denote valley. The inset sketches the recombination process from the interband exciton to the intraband exciton.
• Figure 4: Emission spectra of $X^0$, $X^-$ (see SM), and an exciton interacting with $\nu=1$ in a MoS$_2$ monolayer at $B=10$ T, shown for (a) $T=1$ mK and (b) $T=5$ K.