Unusual Angular Dependence of the Raman Response in Black Phosphorus

Anisotropic materials are characterized by a unique optical response, which is highly polarization-dependent. Of particular interest are layered materials formed by the stacking of two-dimensional (2D) crystals that are naturally anisotropic in the direction perpendicular to the 2D planes. Black phosphorus (BP) is a stack of 213 phosphorene crystals and a highly anisotropic semiconductor with a direct band gap. We show that the angular dependence of polarized Raman spectra of BP is rather unusual and can be explained only by considering complex values for the Raman tensor elements. This result can be traced back to the electron photon and electron-phonon interactions in this material.