Unveiling Defect Physics in Gapped Metals: A Theoretical Investigation into Defect Formation and Electronic Structure Interplay

In materials science, point defects play a crucial role in materials properties. This is particularly well known for the wide band gap insulators where the defect formation/compensation determines the equilibrium Fermi level and generally the doping response of a given material. Similarly, the main defect trends are also widely understood for regular metals (e.g., Cu and Zn discussed herein). With the development of electronic structure theory, a unique class of quantum materials - gapped metals (e.g., Ca6Al7O16, SrNbO3, In15SnO24, and CaN2) that exhibit characteristics of both metals and insulators - has been identified. While these materials have internal band gaps similar to insulators, their Fermi level is within one of the main band edges, giving a large intrinsic free carrier concentration. Such unique electronic structures give rise to unique defect physics, where the formation of acceptor or donor defect directly affects not only the electronic structure but also can substantially shift the Fermi level. Motivated by this, herein, we develop a fundamental first-principles theory of defect formation in gapped metal with a primary focus on accurate calculations of defect formation energy. We demonstrate that due to electron-hole recombination, the formation of acceptor defects in n-type gapped metals results in significant dependence of defect formation energy on supercell size, which we explain by the change of band filling and its effect on the defect formation energetics. To accurately describe defect formation energy, we revisit the phenomenology of band-filling corrections and demonstrate the effect of this correction, accurate potential alignment, and other factors that can affect defect energetics. Thus, this work not only sheds light on the intrinsic properties of gapped metals but, in general, establishes a theoretical foundation for analyzing defects in gapped metals.