  Very recently, a novel two-dimension (2D) MXene, MoSi$_2$N$_4$, was
successfully synthesized with excellent ambient stability, high carrier
mobility, and moderate band gap (Science 369, 670, 2020). In this work, the
intrinsic lattice thermal conductivity of monolayer MoSi$_2$N$_4$ is predicted
by solving the phonon Boltzmann transport equation based on the
first-principles calculations. Despite the heavy atomic mass of Mo and complex
crystal structure, the monolayer MoSi$_2$N$_4$ unexpectedly exhibits a quite
high lattice thermal conductivity over a wide temperature range between 300 to
800 K. At 300 K, its in-plane lattice thermal conductivity is 224
Wm$^{-1}$K$^{-1}$. The detailed analysis indicates that the large group
velocities and small anharmonicity are the main reasons for its high lattice
thermal conductivity. We also calculate the lattice thermal conductivity of
monolayer WSi$_2$N$_4$, which is only a little smaller than that of
MoSi$_2$N$_4$. Our findings suggest that monolayer MoSi$_2$N$_4$ and
WSi$_2$N$_4$ are potential 2D materials for thermal transport in future
nano-electronic devices.
