Many-Body Rashba Spin-Orbit Interaction and Exciton Spin Relaxation in Atomically Thin Semiconductor Structures

TL;DR

Exciton spin relaxation in two-dimensional TMDCs is influenced by spin-orbit interactions that are not captured by traditional one-body descriptions. The authors develop a many-body Rashba mechanism arising from self-consistent out-of-plane fields in inhomogeneous dielectrics, derive a second-quantized Rashba Hamiltonian, and formulate an excitonic Rashba model coupled to exciton-phonon scattering to yield spin-flip dynamics. For MoSe2 on asymmetric dielectrics with small bright-dark exciton splitting, Rashba-driven spin relaxation is ultrafast, spanning sub-picosecond to hundreds of femtoseconds, while MoS2 with larger splitting exhibits far slower relaxation. Dielectric mismatch and interlayer spacing provide strong tunability of the effect, offering a controllable route to engineer exciton spin lifetimes in 2D semiconductors with implications for valleytronics and optoelectronics.

Abstract

We propose a pair spin-orbit interaction (PSOI) mechanism by establishing a mesoscopic many-particle Rashba Hamiltonian. In lowest order, this Hamiltonian self-consistently describes exciton spin relaxation in monolayer transition metal dichalcogenides (TMDC) due to local electric fields caused by spatial asymmetries in the dielectric environment. For a monolayer MoSe$_2$ on a SiO$_2$ substrate above 77$\,$K showing a bright-dark splitting in the meV range, the local electric field causes fast intravalley spin relaxation on a sub-picosecond timescale, whereas it is negligible for other TMDCs with larger bright-dark splitting.

Figures (11)

• Figure 1: Sketch of the sample geometry. $\epsilon_{1/2}$ is the static dielectric constant of substrate/superstrate and $\epsilon_s$ is the dielectric constant of the thin semiconductor, which are separated by a vacuum gap of width $l$. $\hat{\rho}_{\mathbf q}$, cf. Eq. \ref{['eq:ChargeDensityOperator']}, is the charge density and $\hat{E}_{z,\mathbf q}$ is the (operator-valued) electric field induced by surface charges at the boundaries, cf. Eq. \ref{['eq:ElectricFieldConfined']}.
• Figure 2: Local electric field $E_{z,\mathbf q}^{\text{loc}}$ from Eq. \ref{['eq:ElectricFieldLocalExplicit']} for an example MoSe$_2$ monolayer ($\epsilon_{s,\perp} = 7.2$laturia2018dielectric) on a SiO$_2$ substrate ($\epsilon_1=3.9$xue2011scanning, $\epsilon_2=1$) and on a sapphire substrate ($\epsilon_1=\sqrt{\epsilon_{1,\parallel}\epsilon_{1,\perp}}=\sqrt{11.6\cdot 9.4}$fontanella1974low, $\epsilon_2=1$) for a substrate distance $l$ of 0 nm and 0.3 nm.
• Figure 3: Scheme of hole spin coupling between spin-bright A and spin-dark B excitons (a), hole spin coupling between spin-dark A and spin-bright B excitons (b), electron spin coupling between spin-bright and spin-dark A excitons (c) and electron spin coupling between spin-dark B and spin-bright B excitons (d) at the $K$ valley induced by the corresponding Rashba coupling matrix elements $S_{\mathbf Q}^{h/e,K,K}$ in Eq. \ref{['eq:RashbaMatrixElementIntrinsicHole']} and Eq. \ref{['eq:RashbaMatrixElementIntrinsicElectron']}.
• Figure 4: Alignment of the respective local electric field $E_{z,\mathbf q}^{\text{loc},i}$ induced by the individual hole ($i=h$) and electron ($i=e$) of an exciton (shaded ellipse) in a thin semiconductor $\epsilon_s$ for different dielectric environments $\epsilon_1$ and $\epsilon_2$. $E_z^{\text{ext}}$ is an external electric field chosen as polarized in positive $z$-direction.
• Figure 5: Excitonic Rashba matrix element due to local electron-induced fields $E_{z,\mathbf q}^{\text{loc},e}$ ("$e$"), local hole-induced fields $E_{z,\mathbf q}^{\text{loc},h}$ ("$h$") and total local fields ("$e+h$"), cf. Eq. \ref{['eq:LocalElectricField_i']}, from Eq. \ref{['eq:RashbaMatrixElementIntrinsicElectron']} for interlayer distances $l$ of 0 nm and 0.3 nm (blue and red coloring) in a MoSe$_2$ monolayer on a sapphire substrate. "ext" denotes the external contribution from Eq. \ref{['eq:RashbaMatrixElementIntrinsicElectron']}, where the magnitude of the external field $E_z^{\text{ext}}$ is chosen to match the total local-field interaction strength ("$e+h$").