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In this work, we present an atomistic first-principles framework for modelingthe low-temperature electronic and transport properties of disorderedtwo-dimensional (2D) materials with randomly distributed point defects(impurities). The method is based on the $T$-matrix formalism in combinationwith realistic density-functional theory (DFT) descriptions of the defects andtheir scattering matrix elements. From the $T$-matrix approximations to thedisorder-averaged Green's function (GF) and the collision integral in theBoltzmann transport equation, the method allows calculations of, e.g., thedensity of states (DOS) including contributions from bound defect states, thequasiparticle spectrum and the spectral linewidth (scattering rate), and theconductivity/mobility of disordered 2D materials. We demonstrate the method byexamining these quantities in monolayers of the archetypal 2D materialsgraphene and transition metal dichalcogenides (TMDs) contaminated with vacancydefects and substitutional impurity atoms. By comparing the Born and $T$-matrixapproximations, we also demonstrate a strong breakdown of the Bornapproximation for defects in 2D materials manifested in a pronouncedrenormalization of, e.g., the scattering rate by the higher-order $T$-matrixmethod. As the $T$-matrix approximation is essentially exact for dilutedisorder, i.e., low defect concentrations ($c_\text{dis} \ll 1$) or density($n_\text{dis}\ll A_\text{cell}^{-1}$ where $A_\text{cell}$ is the unit cellarea), our first-principles method provides an excellent framework for modelingthe properties of disordered 2D materials with defect concentrations relevantfor devices.

Atomistic $T$-matrix theory of disordered 2D materials: Bound states, spectral properties, quasiparticle scattering, and transport