This paper demonstrates a novel method for measuring the full phonon dispersion along the stacking direction in nanoscale van der Waals materials using picosecond acoustics. A heterostructure of hexagonal boron nitride (hBN) sandwiching black phosphorus (BP) was used. Photoexcitation generates a strain pulse in BP, which propagates into the hBN, reflects at the interface, and creates echoes. Analyzing these echoes reveals the frequency-dependent time-of-flight and group velocity dispersion, effectively mapping the phonon dispersion. First-principles calculations support the experimental findings.

Seong-Yeon Lee, Soungmin Bae, Seonyeong Kim, Suyong Jung, Kenji Watanabe, Takashi Taniguchi, Hannes Raebiger, Ki-Ju Yee