At lower temperatures, as thermal agitation decreases, electrons can arrange themselves into ordered states, leading to distinctive material properties like magnetism and superconductivity. In the 1960s, the concept of the ‘excitonic insulator’ was introduced as an ordered state of electron-hole pairs. This phase can be observed in narrow-gap semiconductors or band-overlapped semimetals, where electrons from the conduction band and holes from the valence band bind together to form an ordered state, known as excitonic order, due to Coulomb interaction. Until the recent breakthroughs in experimental condensed matter physics, excitonic insulators remained primarily a theoretical concept.

Now, a review paper published in the Journal of the Physical Society of Japan introduces the excitonic insulator state via a simple theoretical model that can describe the crossover from a weakly bound electron-hole pairing state to an ordered state of tightly bound pairs, associated with the Bardeen-Cooper-Schrieffer (BCS)–Bose-Einstein condensation (BEC) crossover.

The current review presents theoretical models, such as the spinless Falicov-Kimball Model and the Multi-Orbital Hubbard Model, to investigate excitonic insulator states in strongly correlated electron systems. It also highlights potential candidate materials, including layered transition-metal chalcogenides and various cobalt oxides, along with experimental characterization techniques like photoemission and pump-probe spectroscopy used to study their excitonic states.

Furthermore, the study discusses collective modes, which consider both excitonic order and lattice order, and can help differentiate excitonic effects from lattice distortions. This distinction is crucial for accurately identifying the excitonic insulator state.

The study also mentions identifying potential new candidate systems exhibiting excitonic insulator states, particularly strongly correlated electron systems and materials with tunable band gaps. As research on exploring the excitonic insulators progresses, these insights can lead to significant breakthroughs in the field of materials science and quantum technology.

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