Momentum-resolved dielectric response of free-standing mono-, bi- and tri- layer black phosphorus.

Black phosphorus (BP), a 2D semiconducting material of interest in electronics and photonics, exhibits physical properties characterized by strong anisotropy and band gap energy that scales with reducing layer number. However, the investigation of its intrinsic properties is challenging because thin-layer BP is photo-oxidized under ambient conditions and the energy of its electronic states shifts in different dielectric environments. We prepared free-standing samples of few-layer BP under glovebox conditions and probed the dielectric response in a vacuum using scanning transmission electron microscopy and electron energy loss spectroscopy (STEM-EELS). Thresholds of the excitation energy are measured at 1.9, 1.4, and 1.1 eV for the mono-, bi-, and trilayer BP, respectively, and these values are used to estimate the corresponding optical band gaps. A comparison of our results with electronic structure calculations indicates that the variation of the quasi-particle gap is larger than that of the exciton binding energy. The dispersion of the plasmons versus momentum for one- to three-layer BP and bulk BP highlights a deviation from parabolic to linear dispersion and strong anisotropic fingerprints.