Higher manganese silicide(HMS)has been studied for several decades as a p-type thermoelectric material that is made of non-toxic and earth-abundant elements.Among its attractive properties for high-temperature thermoelectric power generation,HMS is characterized with good chemical,thermal,and mechanical stability at elevated temperatures and in reactive gases.Moreover,the complex Nowontny Chimney Ladder(NCL)crystal structure of HMS gives rise to already very low and anisotropic thermal conductivity even in HMS crystals.Although the thermoelectric properties of HMS materials of different impurity doping have been obtained from past studies,there is a lack of fundamental understanding of the phonon dynamics including the phonon dispersion in the complex NCL structure,and it is unclear whether the already low lattice thermal conductivity of HMS can be suppressed much further.Here I will review the recent efforts of my co-workers in obtaining the phonon dispersion of HMS crystals from inelastic neutron scattering measurements and density functional theory calculation,and in suppressing the HMS thermal conductivity by elemental substitution and in nanostructures.These studies suggest the presence of numerous low-lying optical phonon branches in the complex NCL structure,especially a very low-lying twisting polarization of the Si ladder in the Mn chimney.The twisting polarization undergoes several avoided crossing with the three acoustic branches,and is expected to scatter the acoustic phonons.In addition,the anisotropic thermal conductivity found in HMS crystals is mainly caused by the anisotropy in the group velocity.The obtained phonon dispersion is further used to suggest that glass-like thermal conductivity can be obtained in nanostructured HMS with a grain size of about 10 nm without reducing the thermoelectric power factor.While this prediction is being examined by experiments with both individual HMS nanostructures and nanocrystalline bulk HMS,partial substitution of Mn with heavier Re has been used to obtain a thermal conductivity approaching the amorphous limit at high temperatures.