Observation of the nonanalytic behavior of optical phonons in monolayer hexagonal boron nitride

Phonon splitting of the longitudinal and transverse optical modes (LO-TO splitting), a ubiquitous phenomenon in three-dimensional polar materials, will break down in two-dimensional (2D) polar systems. Theoretical predictions propose that the LO phonon in 2D polar monolayers becomes degenerate with the TO phonon, displaying a distinctive "V-shaped" nonanalytic behavior near the center of the Brillouin zone. However, the full experimental verification of these nonanalytic behaviors has been lacking. Here, using monolayer hexagonal boron nitride (h-BN) as a prototypical example, we report the comprehensive and direct experimental verification of the nonanalytic behavior of LO phonons by inelastic electron scattering spectroscopy. Interestingly, the slope of the LO phonon in our measurements is lower than the theoretically predicted value for a freestanding monolayer due to the screening of the Cu foil substrate. This enables the phonon polaritons in monolayer h-BN/Cu foil to exhibit ultra-slow group velocity (similar to 5 x 10(-6) c, c is the speed of light) and ultra-high confinement (similar to 4000 times smaller wavelength than that of light). These exotic behaviors of the optical phonons in h-BN presents promising prospects for future optoelectronic applications.