# Diffusive nature of thermal transport in stanene

Using the phonon Boltzmann transport formalism and density functional theory based calculations, we show that stanene has a low thermal conductivity. For a sample size of 1$\times$1 $\mu$m$^{2}$ ($L\times W$), the lattice thermal conductivities along the zigzag and armchair directions are 10.83 W/m-K and 9.2 W/m-K respectively, at room temperature, indicating anisotropy in the thermal transport. The low values of thermal conductivity are due to large anharmonicity in the crystal resulting in high Gr\"{u}neisen parameters, and low group velocities. The room temperature effective phonon mean free path is found to be around 17 nm indicating that the thermal transport in stanene is completely diffusive in nature. Furthermore, our study brings out the relative importance of the contributing phonon branches and reveals that, at very low temperatures, the contribution to lattice thermal conductivity comes from the flexural acoustic (ZA) branch and at higher temperatures it is dominated by the longitudinal acoustic (LA) branch. We also show that lattice thermal conductivity of stanene can further be reduced by tuning the sample size and creating rough surfaces at the edges. Such tunability in the lattice thermal conductivity in stanene suggests its applications in thermoelectric devices.

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