Theoretical Study: Challenges Associated with Rare-Earth-Based Superconducting Materials - Marim Algodi (AlQalam Journal of Medical and Applied Sciences, 2026)
Rare-earth (RE) elements are crucial in the advancement of high-temperature superconductors, ranging from the well-known RE-Ba-Cu-O (REBCO) cuprates to the recently discovered high-pressure rare-earth polyhydrides. This theoretical study delves into the fundamental challenges encountered when integrating rare-earth elements into superconducting lattices. We specifically address the inherent antagonism between the local magnetic moments of 4f electrons and the formation of Cooper pairs, the complexities involved in modeling highly correlated electronic states, and the stringent structural stability requirements for high-T_c phases. Through a comprehensive analysis of existing literature and advanced theoretical models, including the Abrikosov-Gorkov theory and Density Functional Theory (DFT) with Hubbard corrections (DFT+U), we pinpoint the critical factors that either limit or enhance superconductivity in these intricate systems. Our findings indicate that while non-magnetic rare-earth elements such as Lanthanum (La) and Yttrium (Y) facilitate the highest transition temperatures (T_c) in hydride systems, the magnetic rare-earth series offers a unique platform for exploring the coexistence of magnetism and superconductivity, despite presenting substantial theoretical and experimental hurdles. This paper aims to provide a foundational understanding of these challenges and propose future research directions to overcome them, ultimately contributing to the quest for room-temperature superconductivity.