Ultralow thermal conductivity in two-dimensional MoO$_3$

Monolayer molybdenum trioxide (MoO$_3$) is an emerging two-dimensional (2D) material with high electrical conductivity. Using first-principles calculations and a Boltzmann transport theoretical framework, we predict record low room-temperature phonon thermal conductivity ($\kappa_p$) of 1.57 W/mK and 1.26 W/mK along the principal in-plane directions of MoO$_3$ monolayer. The behavior is attributed to the combination of soft flexural and in-plane acoustic modes, which are coupled through the finite layer thickness, and to the strong bonding anharmonicity, which gives rise to significant 3- and 4-phonon scattering events. These insights suggest new indicators for guiding the search of 2D materials with low $\kappa_p$. Our result motivates experimental $\kappa_p$ measurements in MoO$_3$, and its applications as a thermoelectric and thermally protective material.