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Coulomb interaction and its screening play an important role in many physicalphenomena of materials ranging from optical properties to many-body effectsincluding superconductivity. Here, we report on a systematic study ofdielectric screening in few-layer black phosphorus (BP), a two-dimensionalmaterial with promising electronic and optical characteristics. We use acombination of a tight-binding model and rigorously determined bare Coulombinteractions, which allows us to consider relevant microscopic effects beyondthe long-wavelength limit. We calculate the dielectric function of few-layer BPin the random phase approximation and show that it exhibits stronglyanisotropic behavior even in the static limit. We also estimate the strength ofeffective local and non-local Coulomb interactions and determine their dopingdependence. We find that the $p_z$ states responsible for low-energyexcitations in BP provide a moderate contribution to the screening, weakeningthe on-site Coulomb interaction by less that a factor of two. Finally, wecalculate the full plasmon spectrum of few-layer BP and discuss the effectsbeyond long-wavelengths.

Coulomb interactions and screening effects in few-layer black phosphorus: a tight-binding consideration beyond the long-wavelength limit