Supplement Number 1

Detailed information regarding computational details, band structure with and without spin-orbit coupling, convergence tests on phonon dispersion, convergence tests on third-order interatomic force constants of 2D-GaN, convergence tests on lattice thermal conductivity, convergence tests on fourth-order interatomic force constants of 2D-SiC, electron band structure of 2D-GaN and Fermi energy related to the carrier concentrations, accumulated lattice thermal conductivity, and electron density of states.