Linear scaling quantum transport methodologies

In recent years, predictive computational modeling has become a cornerstone for the study of fundamental electronic, optical, and thermal properties in complex forms condensed matter, including Dirac topological materials. The simulation quantum transport realistic models calls development linear scaling, or order-N, numerical methods, which then enabling tools guiding experimental research supporting interpretation measurements. this review, we describe compare different order-N methods that have been developed during past twenty used extensively to explore phenomena disordered media. We place particular focus on zero-frequency electrical conductivities derived within Kubo–Greenwood​ Kubo–Streda formalisms, illustrate capabilities these tackle quasi-ballistic, diffusive, localization regimes noninteracting limit. issue cost versus accuracy various proposed schemes is addressed depth. usefulness with examples materials, such as polycrystalline defected graphene models, 3D metals semimetals, carbon nanotubes, organic semiconductors. Finally, extend review spin dynamics transport, efficient approaches calculating charge, spin, valley Hall are described.