Full phonon dispersion along the stacking direction in nanoscale van der Waals materials by picosecond acoustics

Phonon dispersion in crystals determines many important material properties, but its measurement usually requires large-scale facilities and is limited to bulk samples. Here, we demonstrate the measurement of full phonon dispersion along the stacking direction in nanoscale systems by using picosecond acoustics. A heterostructure sample was prepared consisting of layers of hexagonal boron nitride (hBN) sandwiching a thin layer of black phosphorus (BP), within which a strain pulse was generated by photoexcitation and observed with an optical probe in the BP layer. The strain pulse traverses to the few nanometer thick hBN layers, where it propagates to the edge and echoes back, like acoustic waves in Newton’s cradle. The echoes returning to the BP layer provide information on the frequency-dependent time-of-flight and group velocity dispersion of the sample system. The microscopic origin of the photoinduced strain pulse generation and its propagation is revealed from first principles. Phonon frequency combs observed in the Fourier transform spectrum confirm the strain wave round trips and demonstrate the feasibility of determining group velocity dispersion through photoacoustics.