Complex Raman Tensor in Helicity-Changing Raman Spectra of Black Phosphorus under Circularly Polarized Light

In anisotropic two-dimensional materials, complex values of Raman tensors are necessary to explain the abnormal linearly polarized Raman spectra. In this work, we measured the helicity-changing Raman spectra of few-layer black phosphorus (BP) excited by circularly polarized light. We observed that the polarized Raman intensities of the A_g modes show a deflection angle that depends on the sample orientation, thickness, and laser excitation energy. To understand the deflection, we calculated the resonant Raman spectra by first-principles calculations, which give complex Raman tensors as a function of laser excitation energy. In particular, the phase difference between the elements of the complex Raman tensor is relevant to the deflection angle. The calculated results of monolayer BP reproduce the experimental helicity-resolved Raman spectra of few-layer BP satisfactorily.