Understanding Iron-Pnictide Superconductors using Muon Spin Rotation and Scanning Tunneling Microscopy with Nonconvex Optimization

Iron-based high temperature superconductors are a large family of materials that exhibit unconventional superconductivity and arise from antiferromagnetically-ordered parent compounds. One of the grand challenges in understanding the behavior of these materials is determining the physical mechanisms responsible for the transition into the superconducting state. This thesis describes two recent investigations to explore the magnetic and superconducting properties of NaFeAs in response to changes in temperature and nickel dopants. The peculiar interplay of magnetism and superconductivity in nickel-doped NaFeAs is elucidated using muon spin rotation. Our experimental findings on this novel system are supported with both computational and theoretical calculations. The second investigation describes an improvement to the analysis framework to the scanning tunneling microscopy technique that leverages recent advances in nonconvex optimization. This novel approach is applied directly to microscopy images of NaFeAs to provide unprecedented phase-sensitive access to the quasiparticle scattering spectrum in the material. These results place constraints on theoretical models that describe the local electronic structure and physics of NaFeAs