  The electronic and thermal transport properties have been systematically
investigated in monolayer C$_4$N$_3$H with first-principles calculations. The
intrinsic thermal conductivity of monolayer C$_4$N$_3$H was calculated coupling
with phonons Boltzmann transport equation. For monolayer C$_4$N$_3$H, the
thermal conductivity (\k{appa}) (175.74 and 157.90 W m-1K-1 with a and b-plane,
respectively) is significantly lower than that of graphene (3500
Wm$^{-1}$K$^{-1}$) and C3N(380 Wm$^{-1}$K$^{-1}$). Moreover, it is more than
the second time higher than C$_2$N (82.88 Wm$^{-1}$K$^{-1}$) at 300 K.
Furthermore, the group velocities, relax time, anharmonicity, as well as the
contribution from different phonon branches, were thoroughly discussed in
detail. A comparison of the thermal transport characters among 2D structure for
monolayer C$_4$N$_3$H, graphene, C$_2$N and C$_3$N has been discussed. This
work highlights the essence of phonon transport in new monolayer material.
