Plasmonic detection of Rashba spin-orbit coupling in monolayer transition-metal dichalcogenides

Abstract

Rashba spin-orbit coupling (RSOC) induces strong momentum-dependent spin splitting and plays a crucial role in fields like spintronics and topological photonics. We here theoretically investigate the collective excitations in monolayer transition metal dichalcogenides (ML-TMDs) hosting RSOC, and conceive an approach to precisely quantify the strength of RSOC using plasmons. We determine the electron energy loss function (EELF) and plasmon dispersions for n-type ML-TMD from the dynamic dielectric function in the framework of the standard random phase approximation (RPA). In this system, both optical and acoustic plasmon modes are observed in the EELF and plasmon dispersions. Moreover, the plasmonic and spectral properties are tunable by electron density and dependent on RSOC. Crucially, we identify a minimum energy gap between the two plasmon modes to serve as a direct spectral signature of the RSOC strength. These results establish plasmons as a non-invasive, precise, and broadly tunable technique for determining RSOC in TMD van der Waals heterostructures and devices.

Figures (3)

• Figure 1: Schematic conduction band profiles of ML-MoS$_2$ in the $K$ valley and the corresponding electron energy loss function (EELF) at fixed electron density $n_e= 2 \times 10^{12}~\mathrm{cm}^{-2}$. (a) and (c) without RSOC; (b) and (d) including RSOC. Red and blue arrows indicate the spin textures in different subbands. A characteristic minimum energy gap $\Omega_R$ between the bottom of the optical plasmon mode and the top of the acoustic plasmon mode, serves as a fingerprint of the RSOC.
• Figure 2: The EELF, plasmon dispersion, and corresponding Fermi occupation in $n$-type ML-MoS$_2$. (a)$-$(c) For fixed electron density of $n_e= 1 \times 10^{12}~\mathrm{cm}^{-2}$, with RSOC strengths $\lambda_R =$ 10, 30, and 60 meV, as labeled. (d)$-$(f) For fixed RSOC strength $\lambda_R$ =20 meV, with electron densities $n_e= 1 \times 10^{12}~\mathrm{cm}^{-2}$, $2 \times 10^{12}~\mathrm{cm}^{-2}$, and $3 \times 10^{12}~\mathrm{cm}^{-2}$, as labeled. The white shaded regions indicate the intra- and intersubband $e$-$h$ continua.
• Figure 3: The minimum energy gap $\Omega_R$ separating the two plasmon modes and the plasmon energy $\Omega^+_{q=0}$ of the optical plasmon mode at $q\rightarrow0^+$, as a function of RSOC strength $\lambda_R$, for an $n$-type ML-MoS$_2$ at different electron densities $n_e =1 \times 10^{12}~\mathrm{cm}^{-2}$ (blue), $2 \times 10^{12}~\mathrm{cm}^{-2}$ (yellow), and $3 \times 10^{12}~\mathrm{cm}^{-2}$ (red).