Computational materials research is steadily moving from pure characterization towards discovery and design of optimal materials. We are using it to design, characterize and optimize superconductors for use under extreme conditions of high fields or frequencies. We tailor superconductors so that vortices nucleate at fields much higher than the lower critical field, and so that they dissipate less power at high frequencies. We model the effects of impurities into thin surface layers of superconductors to increase their quality at high surface fields. Superconducting radio-frequency (SRF) cavities for particle accelerators are important for technological applications and serve as testbeds and experimental validation for our theoretical predictions of superconducting materials under extreme conditions.

With the Sethna group at Cornell (as part of the Center for Bright Beams), I have shown that crystal anisotropy (common in high-T_c superconductors) does not significantly affect the superheating field near T_c for most type-II superconductors [read more] (the superheating field is nearly isotropic in the yellow region of the diagram on (a)). This result is relevant to the assessment of layered materials such as MgB₂ and iron pnictides. I have also developed an 'instanton' calculation of disorder-mediated vortex nucleation to show that the increased susceptibility to dirt due to the smaller coherence lengths of next-generation cavity materials is swamped by much stronger effects in the proximity of the superheating field [read more]. Our topical review [read more] summarizes theoretical calculations of the superheating field for semi-infinite superconductors subject to a field parallel to its surface. More recently, I have explained the hysteretic mechanisms that are responsible for the field-dependent residual losses of SRF cavities due to the motion of isolated trapped vortex lines under the action of parallel oscillating fields at the surface [read more]. By invoking collective weak pinning theory in the context of a model of vortex dynamics (illustrated in (b)), we make simple estimates, approximate analytical calculations, and numerical simulations that compare well with cavity tests performed in CERN and Cornell. Our simple formulas describing power losses and crossover behavior can be used to guide the tuning of material parameters to optimize cavity performance.