Observation of the Breakdown of Optical Phonon Splitting in a Two-dimensional Polar Monolayer

Abstract: Phonon splitting of the longitudinal optical and transverse optical modes (LO-TO splitting), a ubiquitous phenomenon in three-dimensional (3D) polar materials, is essential for the formation of the 3D phonon polaritons. Theories predict that the LO-TO splitting will break down in two-dimensional (2D) polar systems, but direct experimental verification is still missing. Here, using monolayer hexagonal boron nitride (h-BN) as a prototypical example, we report the direct observation of the breakdown of LO-TO splitting and the finite slope of the LO phonons at the center of the Brillouin zone in 2D polar materials 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 (PhPs) in monolayer h-BN/Cu foil to exhibit ultra-slow group velocity (~ 5 x 10^-6 c, c is the speed of light) and ultra-high confinement (~ 4000 times smaller wavelength than that of light). Our work reveals the universal law of the LO phonons in 2D polar materials and lays a physical foundation for future research on 2D PhPs.