Long-lived Spin Relaxation and Spin Coherence of Electrons in Monolayer MoS$_{\mathrm{2}}$*

Monolayer MoS$_{\mathrm{2}}$ and related transition metal dichalcogenides (TMDs) are direct-gap semiconductors in which strong spin-orbit coupling and a lack of structural inversion symmetry give rise to new coupled spin--valley physics. Although robust spin and valley degrees of freedom have been inferred from polarized photoluminescence (PL) studies of \textit{excitons}, PL timescales are necessarily constrained by short (3--100 ps) electron--hole recombination. Direct probes of spin/valley dynamics of resident carriers in electron (or hole)-doped TMDs, which may persist long after recombination ceases, are still at an early stage. Here we directly measure the coupled spin-valley dynamics of \textit{resident} electrons in $n$-type monolayer MoS$_{\mathrm{2}}$ using optical Kerr-rotation spectroscopy [1], and reveal very long spin lifetimes exceeding 3ns at 5K (orders of magnitude longer than typical exciton lifetimes). In contrast with conventional III-V or II-VI semiconductors, spin relaxation accelerates rapidly in small transverse magnetic fields. This suggests a novel mechanism of electron spin dephasing in monolayer TMDs, driven by rapidly-fluctuating internal spin-orbit fields due to fast intervalley scattering. Additionally, a small but very long-lived oscillatory signal is observed, indicating spin coherence of localized states [2]. These studies provide direct insight into the physics underpinning the spin and valley dynamics of electrons in monolayer TMDs. [1] L. Yang \textit{et al}., \textit{Nature Physics} \textbf{11}, 830 (2015). [2] L. Yang \textit{et al}., \textit{submitted.}