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

TL;DR

This paper introduces a first-principles atomistic $T$-matrix approach to accurately model electronic, spectral, and transport properties of disordered 2D materials with point defects, surpassing traditional approximations.

Contribution

The work develops a realistic $T$-matrix based framework combining DFT and Green's functions to analyze disorder effects in 2D materials, including bound states and scattering.

Findings

The $T$-matrix method captures defect-induced bound states and spectral features.

Higher-order $T$-matrix approximations significantly differ from Born approximation results.

The approach is effective for low defect concentrations relevant to device applications.

Abstract

In this work, we present an atomistic first-principles framework for modeling the low-temperature electronic and transport properties of disordered two-dimensional (2D) materials with randomly distributed point defects (impurities). The method is based on the $T$-matrix formalism in combination with realistic density-functional theory (DFT) descriptions of the defects and their scattering matrix elements. From the $T$-matrix approximations to the disorder-averaged Green's function (GF) and the collision integral in the Boltzmann transport equation, the method allows calculations of, e.g., the density of states (DOS) including contributions from bound defect states, the quasiparticle spectrum and the spectral linewidth (scattering rate), and the conductivity/mobility of disordered 2D materials. We demonstrate the method by examining these quantities in monolayers of the archetypal 2D materials graphene and transition metal dichalcogenides (TMDs) contaminated with vacancy defects and substitutional impurity atoms. By comparing the Born and $T$-matrix approximations, we also demonstrate a strong breakdown of the Born approximation for defects in 2D materials manifested in a pronounced renormalization of, e.g., the scattering rate by the higher-order $T$-matrix method. As the $T$-matrix approximation is essentially exact for dilute disorder, 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 cell area), our first-principles method provides an excellent framework for modeling the properties of disordered 2D materials with defect concentrations relevant for devices.