Soft phonon modes driven huge difference on lattice thermal conductivity between topological semimetal WC and WN

Topological semimetals are currently attracting increasing interest due to their potential applications in topological qubits and low-power electronics, which are closely related to their thermal transport properties. In this work, by solving the Boltzmann transport equation based on first-principles calculations, we systematically investigate the phonon transport properties of topological semimetal WC and WN. The predicted room-temperature lattice thermal conductivities of WC (WN) along a and c directions are 1140.64 (7.47) $\mathrm{W m^{-1} K^{-1}}$ and 1214.69 (5.39) $\mathrm{W m^{-1} K^{-1}}$. Considering the similar crystal structure of WC and WN, it is quite interesting to find that the thermal conductivity of WC is more than two orders of magnitude higher than that of WN. It is found that, different from WN, the large acoustic-optical (a-o) gap prohibits the acoustic+acoustic$\rightarrow$optical (aao) scattering, which gives rise to very long phonon lifetimes, leading to ultrahigh lattice thermal conductivity in WC. For WN, the lack of a-o gap is due to soft phonon modes in optical branches, which can provide more scattering channels for aao scattering, producing very short phonon lifetimes. Further deep insight can be attained from their different electronic structures. Distinctly different from that in WC, the density of states (DOS) of WN at the Fermi level becomes very sharp, which leads to destabilization of WN, producing soft phonon modes. It is found that the small shear modulus $G$ and $C_{44}$ limit the stability of WN, compared with WC. Our works provide valuable information for phonon transports in WC and WN, and motivate further experimental works to study their lattice thermal conductivities.
7 pages, 9 figures