Quantified degeneracy, entropy, and metal-insulator transition in complex transition-metal oxides

Understanding complex correlated oxides and their phase transitions has long been a challenge. The difficulty largely arises from the intriguing interplay between multiple degrees of freedoms. While degeneracy can play an important role in determining material characteristics, there is no well-defined way to quantify and to unveil its role in real materials having complicated band structures. Here we suggest a way to quantify the “effective degeneracy” relevant to metal-insulator transition by introducing entropylike terms. This new quantity well describes the electronic behaviors of transition-metal oxides as a function of external and internal parameters. With 3d titanates, 4d ruthenates, and 5d iridates as our examples, we show that this new effective quantity provides useful insights to understand these systems and their phase transitions. For LaTiO3/LaAlO3 superlattice, we suggest a novel “degeneracy control” metal-insulator transition.