Impurity scattering and Friedel oscillations in mono-layer black phosphorus

TL;DR

This paper investigates how impurity scattering influences local electronic properties and Friedel oscillations in monolayer black phosphorus, revealing anisotropic LDOS features and impurity-induced midgap states.

Contribution

It provides a detailed analysis of impurity effects in BP using numerical and analytical methods, highlighting anisotropic LDOS and impurity-induced midgap states.

Findings

LDOS exhibits strong anisotropy in BP

Midgap states appear within the band gap due to impurities

Impurity potential affects the charge carrier binding and midgap state peaks

Abstract

We study the effect of impurity scattering effect in black phosphorurene (BP) in this work. For single impurity, we calculate impurity induced local density of states (LDOS) in momentum space numerically based on tight-binding Hamiltonian. In real space, we calculate LDOS and Friedel oscillation analytically. LDOS shows strong anisotropy in BP. Many impurities in BP are investigated using $T$-matrix approximation when the density is low. Midgap states appear in band gap with peaks in DOS. The peaks of midgap states are dependent on impurity potential. For finite positive potential, the impurity tends to bind negative charge carriers and vise versa. The infinite impurity potential problem is related to chiral symmetry in BP.