Imaging Novel States in Unconventional Superconductors

Recent advances in the development of Josephson scanning tunneling spectroscopy (JSTS) have opened a path to explore unconventional superconductivity. Since experimental efforts have demonstrated the capability to perform atomically resolved measurements of the Josephson critical current, we theoretically show that this critical current is able to image the spatial superconducting order parameter (SCOP) across a wide range of conventional and unconventional superconductors. Because the SCOP is often a fingerprint of superconducting states and phases, including the triplet superconductivity associated with topological Majorana modes, its characterization with JSTS offers a unique way to identify novel superconducting phenomena that might otherwise be inaccessible. In the case of topological superconductivity, experimental identification of non-triviality is problematic because its spectroscopic evidence can be mixed with trivial in-gap states. As I demonstrate, however, an equilibrium transport measurement offers a qualitatively distinct route to identify topological currents.