Challenges and opportunities for applications of unconventional superconductors

Since the discovery of high-$T_c$ cuprates the quest for new superconductors has shifted toward more anisotropic, strongly correlated materials with lower carrier densities and competing magnetic and charge density wave orders. While these materials features enhance superconducting correlations, they also result in serious problems for applications at liquid nitrogen (and higher) temperatures and strong magnetic fields, so that such conventional characteristics as the critical temperature $T_c$ and the upper critical field $H_{c2}$ are no longer the main parameters of merit. This happens because of strong fluctuations of the order parameter, thermally-activated hopping of pinned vortices and electromagnetic granularity, as has been established after extensive investigations of cuprates and Fe-based superconductors. In this paper I give an overview of these mechanisms crucial for power and magnet applications and discuss the materials restrictions which have to be satisfied in order to make superconductors useful at high temperatures and magnetic fields. These restrictions become more and more essential at higher temperatures and magnetic fields, particularly for the yet-to-be-discovered superconductors operating at room temperatures. In this case the performance of superconductors will be limited by destructive fluctuations of the order parameter so higher superfluid density and weaker electronic anisotropy which reduce these fluctuations can become far more important than higher $T_c$.