Real-space superconducting properties in the atomically-thin limit: Ab initio approach and its application to Josephson junctions

Abstract

Real-space superconducting properties are increasingly important to characterize low-dimensional, layered, and nanostructured materials. Here, we present a method to extract the real-space superconducting order parameter from the superconducting gap spectrum obtained via anisotropic Migdal-Eliashberg calculations, using the Bloch wave functions of the Fermi states. We apply this approach to a selection of atomically thin material systems. Our analysis of gallenene, a monolayer of gallium atoms, shows that its planar and buckled phases exhibit distinct superconducting order parameter behaviors, shaped by their structural and electronic properties. Furthermore, we demonstrate that our real-space approach is exceptionally suited to identify and characterize Josephson junctions made from van der Waals materials. Our examination of a bilayer of NbSe$_2$ reveals that the van der Waals gap acts as an intrinsic weak link between the superconducting NbSe$_2$ layers. Therefore, a bilayer of NbSe$_2$ represents one of the thinnest and most tunable Josephson junction architectures, with potential applications in quantum devices. Our findings underscore the utility of transformation into real-space in understanding superconducting properties through ab initio calculations.