Unambiguous determination of crystal orientation in black phosphorus by angle-resolved polarized Raman spectroscopy

Angle-resolved polarized Raman spectroscopy (ARPRS) is widely used to determine the crystal orientations of anisotropic layered materials (ALMs), which is an essential step to study all of their anisotropic properties. However, the understanding of the ARPRS response of black phosphorous (BP) as a most widely studied ALM is still unsatisfactory. Here, we clarify two key controversies about the physical origin of the intricate ARPRS response and the determination of crystal orientations in BP. Through systematic ARPRS measurements, we show that the degree of anisotropy of the response evolves gradually and periodically with the BP thickness, eventually leading to the intricate response. Meanwhile, we find that using the Raman peak intensity ratio of the two A_g phonon modes, the crystal orientations of BP can be unambiguously distinguished via a concise inequality . Comprehensive analysis and first-principles calculations reveal that the external anisotropic interference effect and the intrinsic electron-phonon coupling are responsible for the observations.