  An increasing number of two-dimensional (2D) materials have already been
achieved experimentally or predicted theoretically, which have potential
applications in nano- and opto-electronics. Various applications for electronic
devices are closely related to their thermal transport properties. In this
work, the strain dependence of phonon transport in monolayer SiC with a perfect
planar hexagonal honeycomb structure is investigated by solving the linearized
phonon Boltzmann equation. It is found that room-temperature lattice thermal
conductivity ($\kappa_L$) of monolayer SiC is two orders of magnitude lower
than that of graphene. The low $\kappa_L$ is due to small group velocities and
short phonon lifetimes, which can also be explained by polarized covalent bond
due to large charge transfer from Si to C atoms. In considered strain range, it
is proved that the SiC monolayer is mechanically and dynamically stable. With
increased tensile strain, the $\kappa_L$ of SiC monolayer shows an unusual
nonmonotonic up-and-down behavior, which is due to the competition between the
change of phonon group velocities and phonon lifetimes of low frequency phonon
modes. At low strains ($<$8\%), the phonon lifetimes enhancement induces the
increased $\kappa_L$, while at high strains ($>$8\%) the reduction of group
velocities as well as the decrease of the phonon lifetimes are the major
mechanism responsible for decreased $\kappa_L$. Our works further enrich
studies on phonon transports of 2D materials with a perfect planar hexagonal
honeycomb structure, and motivate farther experimental studies.
