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

Bulk black phosphorus (BP) consists of puckered layers of phosphorus atoms. Few-layer BP, obtained from bulk BP by exfoliation, is an emerging candidate as a channel material in post-silicon electronics. A deep understanding of its physical properties and its full range of applications are still being uncovered. In this paper, we present a theoretical and experimental investigation of phonon properties in few-layer BP, focusing on the low-frequency regime corresponding to interlayer vibrational modes. We show that the interlayer breathing mode A(3)g shows a large redshift with increasing thickness; the experimental and theoretical results agree well. This thickness dependence is two times larger than that in the chalcogenide materials, such as few-layer MoS2 and WSe2, because of the significantly larger interlayer force constant and smaller atomic mass in BP. The derived interlayer out-of-plane force constant is about 50% larger than that of graphene and MoS2. We show that this large interlayer force constant arises from the sizable covalent interaction between phosphorus atoms in adjacent layers and that interlayer interactions are not merely of the weak van der Waals type. These significant interlayer interactions are consistent with the known surface reactivity of BP and have been shown to be important for electric-field induced formation of Dirac cones in thin film BP.