From quantum computers to particle accelerators, superconducting materials are a class of material advancing the development of many modern technologies in ambitious ways. In particle accelerators, superconducting radiofrequency (SRF) cavities offer the most profitable advantages and one of the central goals within the field of SRF research is to improve the underlying technology to make SRF cavities accessible and affordable for commercial-grade particle accelerators. Optimizing recipes for SRF cavities requires carefully-designed experiments, which will reveal new phenomena for theorists to resolve, and requires new theories to suggest and inform further experiments. In this dissertation, we provide a glimpse into this perpetual feedback loop from the theorist's point of view. Specifically, we study electron–phonon mediated superconductors niobium and Nb₃Sn and investigate properties of these superconducting materials near interfaces, both internal (grain boundaries) and external (surfaces), where these interfacial defects complicate standard descriptions of bulk superconducting properties.

We begin with a continuum description of a superconductor at mesoscopic length-scales using the Bogoliubov-de Gennes method and propose a three-fluid model of dissipation at superconducting surfaces. There, we compute scattering times of Bogoliubov quasiparticles with impurities having scattering strengths informed by ab initio calculations. Then, we treat microscopic interactions more rigorously by working primarily with ab initio methods to model systems with realistic atomic structures using density-functional theory (DFT) and the associated Wannier interpolation techniques to compute refined many-body interactions. We present the first comprehensive ab initio study of grain boundaries in Nb₃Sn, where we investigate how grain boundaries impact the electronic structure, defect-segregation behavior, and superconducting properties in the material. In addition, we provide a model for a local T_c and propose a way to predict flux-pinning force densities from DFT calculations. Adding in more microscopic details, we proceed to investigations of electron–phonon coupled properties, where we show how phonon and electron–phonon coupled properties manifest at the Nb(100) surface and the (3×1)-O/Nb(100) oxide-reconstructed surface in relation to the corresponding properties in bulk niobium. We then introduce the experimental method of helium atom scattering and explain how this technique can probe electron–phonon coupling at a surface of a superconductor. Afterwards, we reveal the first fully ab initio framework to compute inelastic atom–surface scattering intensities that rigorously evaluates the interaction between the surface electrons and the scattering atom, which we compute within a Wannier function basis. We present the predictions of this new method alongside helium scattering measurements and compare the results against two lower levels of theory to demonstrate the improvement among predictions. We conclude with a brief outlook regarding the topics and methods encountered throughout this dissertation, and we emphasize that most of the underlying theoretical approaches we present here are suitable for a wide range of applications and materials, both superconducting and normal-conducting.