Efficient Multiscale Lattice Simulations of Strained and Disordered Graphene

Abstract

Abstract Graphene's electronic and structural properties are often studied using continuum models, such as the Dirac Hamiltonian for its electronic properties or the Born von Karman plate theory for its structural or elastic properties. While long-wavelength continuum approaches generally provide a convenient and accurate theoretical framework to understand graphene, in many scenarios of interest, it is desirable to resort to lattice models accounting for short-range bond transformation effects, eg, induced by defects or chemical substitutions. Here, we present an efficient multiscale methodology that combines information from first-principles calculations and long-range continuum strain fields to inform accurate real-space tight-binding Hamiltonians capturing the effect of both short-range disorder and long-range strains. Efficient numerical algorithms based on Lanczos recursion and kernel polynomial methods are used to extract physical observables of interest in realistic system sizes containing in excess of tens of millions of atoms.