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Topological semimetal may have potential applications like topologicalqubits, spintronics and quantum computations. Efficient heat dissipation is akey factor for the reliability and stability of topological semimetal-basednano-electronics devices, which is closely related to high thermalconductivity. In this work, the elastic properties and lattice thermalconductivity of TaN are investigated by first-principles calculations and thelinearized phonon Boltzmann equation within the single-mode relaxation timeapproximation (RTA). According to the calculated bulk modulus, shear modulusand $C_{44}$, TaN can be regarded as a potential incompressible and hardmaterial. The room-temperature lattice thermal conductivity is predicted to be838.62 $\mathrm{W m^{-1} K^{-1}}$ along a axis and 1080.40 $\mathrm{W m^{-1}K^{-1}}$ along c axis, showing very strong anisotropy. It is found that thelattice thermal conductivity of TaN is several tens of times higher than one ofother topological semimetal, such as TaAs, MoP and ZrTe, which is due to verylonger phonon lifetimes for TaN than other topological semimetal. The verydifferent atomic masses of Ta and N atoms lead to a very large acoustic-opticalband gap, and then prohibits the scattering between acoustic and optical phononmodes, which gives rise to very long phonon lifetimes. Based on mass differencefactor, the WC and WN can be regarded as potential candidates with ultrahighlattice thermal conductivity. Calculated results show that isotope scatteringhas little effect on lattice thermal conductivity, and that phonon with meanfree path(MFP) larger than 20 (80) $\mathrm{\mu m}$ at 300 K has littlecontribution to the total lattice thermal conductivity. This work implies thatTaN-based nano-electronics devices may be more stable and reliable due toefficient heat dissipation.

Ultrahigh lattice thermal conductivity in topological semimetal TaN caused by large acoustic-optical gap