  Phonon scattering by electrons, or "phonon-electron scattering", has been
recognized as a significant scattering channel for phonons in materials with
high electron concentration, such as thermoelectrics and nanoelectronics, even
at room temperature. Despite the abundant previous studies of phonon-electron
scattering in different types of three-dimensional (3D) bulk materials, its
impact on the phonon transport, and thus the heat transfer properties, of
two-dimensional (2D) materials has not been understood. In this work, we apply
ab initio methods to calculate the phonon-electron scattering rates in two
representative 2D materials, silicene and phosphorene, and examine the
potential of controlling the thermal conductivity of these materials via
externally induced phonon-electron scattering by electrostatic gating. We also
develop an analytical model to explain the impact of reduced dimensionality and
distinct electron and phonon dispersions in 2D on phonon-electron scattering
processes. We find that over 40\% reduction of the lattice thermal conductivity
can be achieved in silicene with an induced charge carrier concentration in the
range of $10^{13}~cm^{-2}$, which is experimentally achievable. Our study not
only generates new fundamental insights into phonon transport in 2D materials
but also provides practical guidelines to search for 2D materials with strong
phonon-electron scattering for potential thermal switching applications.
