We present theoretical studies of SRF materials from the Center for Bright Beams. First, we discuss the effects of disorder, inhomogeneities, and materials anisotropy on the maximum parallel surface field that a superconductor can sustain in an SRF cavity, using linear stability in conjunction with Ginzburg-Landau and Eilenberger theory. We connect our disorder mediated vortex nucleation model to current experimental developments of Nb$_3$Sn and other cavity materials. Second, we use time-dependent Ginzburg-Landau simulations to explore the role of inhomogeneities in nucleating vortices, and discuss the effects of trapped magnetic flux on the residual resistance of weakly- pinned Nb$_3$Sn cavities. Third, we present first-principles density-functional theory (DFT) calculations to uncover and characterize the key fundamental materials processes underlying the growth of Nb$_3$Sn. Our calculations give us key information about how, where, and when the observed tin-depletedregions form. Based on this we plan to develop new coating protocols to mitigate the formation of tin depleted regions.
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