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

## TL;DR

This paper investigates dielectric screening and Coulomb interactions in few-layer black phosphorus using a tight-binding approach that extends beyond the long-wavelength limit, revealing anisotropic screening and plasmon behavior.

## Contribution

It introduces a systematic method combining tight-binding and Coulomb interactions to analyze screening effects beyond the long-wavelength approximation in black phosphorus.

## Key findings

- Dielectric function shows strong anisotropy in static limit.
- On-site Coulomb interaction is moderately reduced by p_z states.
- Full plasmon spectrum exhibits features beyond long-wavelength limit.

## Abstract

Coulomb interaction and its screening play an important role in many physical phenomena of materials ranging from optical properties to many-body effects including superconductivity. Here, we report on a systematic study of dielectric screening in few-layer black phosphorus (BP), a two-dimensional material with promising electronic and optical characteristics. We use a combination of a tight-binding model and rigorously determined bare Coulomb interactions, which allows us to consider relevant microscopic effects beyond the long-wavelength limit. We calculate the dielectric function of few-layer BP in the random phase approximation and show that it exhibits strongly anisotropic behavior even in the static limit. We also estimate the strength of effective local and non-local Coulomb interactions and determine their doping dependence. We find that the $p_z$ states responsible for low-energy excitations in BP provide a moderate contribution to the screening, weakening the on-site Coulomb interaction by less that a factor of two. Finally, we calculate the full plasmon spectrum of few-layer BP and discuss the effects beyond long-wavelengths.