Supplementary material: Comparison of uitra-low lattice thermal conductivity of the full Heusler compound Li$_{2}$Rb(Cs)Bi after considering strong quartic anharmonicity

The free energy at different temperatures as a function of time，scattering phase space， mobility changes with doping concentration, the electron scattering rates, and temperature-dependent atomic mean square displacements (MSD) for Li$_{2}$Rb(Cs)Bi.