“…[15][16][17] Recently, there is a progress in managing phonons by nanostructured phononic crystals (PnCs) [18][19][20][21][22][23] which control heat by making use of phononic properties. It heralds the next technological revolution in phononics, such as thermal rectifiers, [15,[24][25][26][27][28][29] optomechanical crystals, [30,31] thermal cloaking, [32][33][34][35][36] thermoelectrics, [37][38][39][40][41] and thermocrystals. [18,21,22] When the characteristic size of nanostructured PnCs is closed to the wavelength of phonons, PnCs may manipulate the phonon band structures which lead to the phonon confinement.…”