Terahertz saturable absorption from relativistic high-temperature thermodynamics in black phosphorus

Due to its tunable infrared band gap and its anisotropic conduction properties, black phosphorus represents a very unique two-dimensional (2D) material, the potential of which in the engineering of new devices still needs to be fully explored. Here, we investigate the nonlinear terahertz (THz) electrodynamics of black phosphorus along the more conducting armchair direction. Similarly to the case of other 2D systems such as graphene and topological insulators, the THz saturable-absorption properties of black phosphorus can be understood within a thermodynamic model by assuming a fast thermalization of the electron bath. While black phosphorus does not display the presence of massless fermions at ambient pressure and temperature, our analysis shows that its anomalous THz nonlinear properties can be accounted for by a relativistic massive Dirac dispersion, provided that the Fermi temperature is low enough. An optimal tuning of the Fermi level therefore represents a strategy to engineer a strong THz nonlinear response in other massive Dirac materials, such as transition-metal dichalchogenides or high-temperature superconductors.