Electric field- and polarisation-dependent two-photon absorption in bilayer black phosphorus

We use an analytical method based on the five-hopping parameter continuous approximate Hamiltonian to theoretically investigate two-photon absorption (TPA) in bilayer black phosphorus (BP) and its dependence on an applied electric field and the polarisation direction of incident light. The results show that there is a threshold value of the energy difference between layers caused by an external electric field, Δ = 1.4625 eV, at which the bandgap of bilayer BP closes. When the electric field intensity is enhanced, but keeping Δ < 1.4625 eV, the absorption peak of TPA increases with a redshift; when Δ > 1.4625 eV, the absorption peak of TPA decreases with a blueshift, and the bandgap reopens around the Γ point. Moreover, the TPA coefficient changes periodically with the polarisation angle of the incident light as a cosine function, making BP a potentially viable linear polariser for applications.