  The electron-phonon coupling strength in the spin-split valence band maximum
of single-layer MoS$_2$ is studied using angle-resolved photoemission
spectroscopy and density functional theory-based calculations. Values of the
electron-phonon coupling parameter $\lambda$ are obtained by measuring the
linewidth of the spin-split bands as a function of temperature and fitting the
data points using a Debye model. The experimental values of $\lambda$ for the
upper and lower spin-split bands at K are found to be 0.05 and 0.32,
respectively, in excellent agreement with the calculated values for a
free-standing single-layer MoS$_2$. The results are discussed in the context of
spin and phase-space restricted scattering channels, as reported earlier for
single-layer WS$_2$ on Au(111). The fact that the absolute valence band maximum
in single-layer MoS$_2$ at K is almost degenerate with the local valence band
maximum at $\Gamma$ can potentially be used to tune the strength of the
electron-phonon interaction in this material.
