Rare-Earth High-Entropy Oxides: Bridging Energy Catalysis and Optoelectronic Innovation

Rare-earth high-entropy oxides (RE-HEOs) represent a distinct class of entropy-stabilized ceramics in which multiple lanthanide cations occupy a common crystallographic sublattice, generating strong chemical disorder, lattice distortion, and complex defect landscapes. Unlike transition-metal-based high-entropy oxides, RE-HEOs are governed by localized 4f electronic states, weak crystal-field coupling, and variable redox chemistry, leading to emergent structural, electronic, magnetic, and optical phenomena that challenge conventional solid-state descriptions. This review provides a physics-oriented analysis of RE-HEOs, focusing on the thermodynamic foundations of configurational entropy stabilization, the interplay between enthalpy, entropy, and kinetic trapping, and the consequences of severe chemical disorder for crystal structure and phase stability. We review how lattice distortion, oxygen vacancy disorder, and cation randomness modify phonon spectra, ionic transport pathways, and electronic structures, with particular emphasis on the role of localized 4f states, defect-induced in-gap levels, and disorder-broadened excitation spectra. Spectroscopic manifestations of disorder including crystal-field relaxation, line broadening, lifetime modification, and energy transfer processes are discussed within a unified framework linking local symmetry breaking to macroscopic response. We further discuss the optoelectronic properties of RE-HEOs, including photoluminescence from intra-4f transitions, upconversion mechanisms, and disorder-induced modifications of radiative lifetimes and quantum efficiency. The application landscape spans both energy conversion (electrocatalysis, solid oxide fuel cells, thermal barrier coatings) and optoelectronic technologies (phosphors, scintillators, optical thermometry, and anti-counterfeiting). Likewise, we assess theoretical and computational approaches, including density functional theory with strong correlation corrections, statistical thermodynamics, and emerging machine-learning models, highlighting their ability and current limitations in capturing disorder-driven physics in multi-component oxides. Finally, we identify open questions central to condensed-matter physics, including the nature of entropy-stabilized metastability, the limits of band theoretical descriptions in highly disordered 4f systems, and the role of configurational entropy in tuning electron-phonon and defect interactions. By consolidating experimental and theoretical insights, this review establishes RE-HEOs as a platform for exploring disorder-dominated solid-state physics beyond conventional crystalline oxides.