Impurity effects in a two--dimensional system with Dirac spectrum

TL;DR

This paper investigates how impurities affect the electronic properties of a two-dimensional Dirac system, revealing resonance states, spectrum rearrangements, and localized states at varying impurity concentrations.

Contribution

It introduces a detailed analysis of impurity-induced resonance states and spectrum restructuring in 2D Dirac systems, highlighting the conditions for gap formation and localization.

Findings

Resonance states appear near the Dirac point at high impurity perturbations.

Spectrum undergoes rearrangement with impurity concentration, forming a quasi-gap.

Localized states remain exponentially small if the critical impurity concentration is not reached.

Abstract

It is demonstrated that in a two--band 2D system the resonance state is manifested close to the energy of the Dirac point in the electron spectrum for the sufficiently large impurity perturbation. With increasing the impurity concentration, the electron spectrum undergoes the rearrangement, which is characterized by the opening of the broad quasi--gap in the vicinity of the nodal point. If the critical concentration for the spectrum rearrangement is not reached, the domain of localized states remains exponentially small compared to the bandwidth.