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I use first principles calculations to investigate the thermal conductivityof $\beta$-In$_2$O$_3$ and compare the results with that of$\alpha$-Al$_2$O$_3$, $\beta$-Ga$_2$O$_3$, and KTaO$_3$. The calculated thermalconductivity of $\beta$-In$_2$O$_3$ agrees well with the experimental dataobtain recently, which found that the low-temperature thermal conductivity inthis material can reach values above 1000 W/mK. I find that the calculatedthermal conductivity of $\beta$-Ga$_2$O$_3$ is larger than that of$\beta$-In$_2$O$_3$ at all temperatures, which implies that $\beta$-Ga$_2$O$_3$should also exhibit high values of thermal conductivity at low temperatures.The thermal conductivity of KTaO$_3$ calculated ignoring thetemperature-dependent phonon softening of low-frequency modes givehigh-temperature values similar that of $\beta$-Ga$_2$O$_3$. However, thecalculated thermal conductivity of KTaO$_3$ does not increase as steeply asthat of the binary compounds at low temperatures, which results in KTaO$_3$having the lowest low-temperature thermal conductivity despite having acousticphonon velocities larger than that of $\beta$-Ga$_2$O$_3$ and$\beta$-In$_2$O$_3$. I attribute this to the fact that the acoustic phononvelocities at low frequencies in KTaO$_3$ is less uniformly distributed becauseits acoustic phonon branches are more dispersive compared to the binary oxides,which causes enhanced momentum loss even during the normal phonon-phononscattering processes. I also calculate thermal diffusivity using thetheoretically obtained thermal conductivity and heat capacity and find that allfour materials exhibit the expected $T^{-1}$ behavior at high temperatures.Additionally, the calculated ratio of the average phonon scattering time toPlanckian time is larger than the lower bound of 1 that has been observedempirically in numerous other materials.

First principles study of thermal conductivity of In$_2$O$_3$ in relation to Al$_2$O$_3$, Ga$_2$O$_3$, and KTaO$_3$