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Bulk black phosphorus (BP) consists of puckered layers of phosphorus atoms.Few-layer BP, obtained from bulk BP by exfoliation, is an emerging candidate asa channel material in post-silicon electronics. A deep understanding of itsphysical properties and its full range of applications are still beinguncovered. In this paper, we present a theoretical and experimentalinvestigation of phonon properties in few-layer BP, focusing on thelow-frequency regime corresponding to interlayer vibrational modes. We showthat the interlayer breathing mode A3g shows a large redshift with increasingthickness; the experimental and theoretical results agreeing well. Thisthickness dependence is two times larger than that in the chalcogenidematerials such as few-layer MoS2 and WSe2, because of the significantly largerinterlayer force constant and smaller atomic mass in BP. The derived interlayerout-of-plane force constant is about 50% larger than that in graphene and MoS2.We show that this large interlayer force constant arises from the sizablecovalent interaction between phosphorus atoms in adjacent layers, and thatinterlayer interactions are not merely of the weak van der Waals type. Thesesignificant interlayer interactions are consistent with the known surfacereactivity of BP, and have been shown to be important for electric-fieldinduced formation of Dirac cones in thin film BP.

Large Frequency Change with Thickness in Interlayer Breathing Mode - Significant Interlayer Interactions in Few Layer Black Phosphorus