Length-dependent lattice thermal conductivity of single-layer and multilayer hexagonal boron nitride: A first-principles study using the Callaway-Klemens and real-space supercell methods

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The phonon dispersion, density of states, Gr\"{u}neisen parameters, and the lattice thermal conductivity of single- and multi-layered boron nitride were calculated using first-principles methods. For the bulk {\it h}-BN we also report the two-phonon density of states. We also present simple analytical solutions to the acoustic vibrational mode-dependent lattice thermal conductivity. Moreover, computations based on the elaborate Callaway-Klemens and the real space super cell methods are presented to calculate the sample length and temperature dependent lattice thermal conductivity of single- and multi-layered hexagonal boron nitride which shows good agreement with experimental data.