Spatial Conductivity Mapping for Identifying Electronically Active Regions in Materials

We discuss the methodology for spatially decomposing the Kubo-Greenwood Formula (KGF) to identify local structures in materials with high/low conduction activity, called space-projected conductivity. The method decomposes the KGF in terms of Kohn-Sham orbitals in real space. A simplified and efficient alternative to SPC, called the N² method, is introduced, which is particularly well-suited for large systems. The method uses the square of the electronic charge density near the Fermi level.  We show the application of these methods in a range of disordered materials – amorphous graphene, amorphous silicon and carbon, amorphous phase-change memory materials, defects in metals, and metal-graphene heterostructures. These tools offer a qualitative new insight into transport in complex materials. The techniques can assist in the development of materials for other applications, such as conducting bridge random access memory (CBRAM), physical unclonable function (PUF) devices, and other systems where atomistic insights into charge transport are essential.