Mott insulator

A material that remains electrically insulating because strong electron–electron repulsion localizes its electrons, even though ordinary band theory predicts metallic conduction.

Hubbard model: A lattice model describing electrons that hop between sites and repel one another when they occupy the same site. It isolates the competition between electron motion and repulsion that produces the insulating state.
Band theory: A framework that explains solids through allowed energy bands formed by electronic states in a periodic structure. Its metallic prediction for a partially filled band creates the puzzle that Mott insulation resolves.
Nickel oxide: An antiferromagnetic insulating compound with the rocksalt crystal structure and chemical formula NiO. NiO is a classic transition-metal oxide whose insulating behavior cannot be explained by simple band filling alone.
Antiferromagnetism: Magnetic order in which neighboring spins align in opposite directions. Localized spins in many Mott insulators order antiferromagnetically through exchange interactions.
Band insulator: An insulator whose filled electronic bands are separated from empty bands by an energy gap. Its gap follows from band filling, unlike the interaction-driven gap central to a Mott insulator.
Mott transition: A transition between metallic and insulating behavior driven by changes in electron interaction strength or related conditions. It describes how changing the balance of hopping and repulsion can destroy or restore conduction.
Bloch theorem: A theorem stating that wavefunctions in a periodic potential have a plane-wave form multiplied by a lattice-periodic function. Periodic crystal structure underlies the extended electronic states assumed in ordinary band descriptions.
Vanadium dioxide: A compound that undergoes a temperature-driven transition between insulating and metallic phases near room temperature. Its metal–insulator transition is a closely studied case involving both electronic correlations and structural change.
High-temperature superconductivity: Superconductivity occurring at temperatures substantially higher than those of conventional metallic superconductors. Doping Mott-insulating cuprates produces superconducting phases whose microscopic origin remains debated.
Charge-transfer insulator: A correlated insulator whose lowest excitation transfers an electron from ligand states to metal states. This competing classification applies when the insulating gap is primarily between oxygen and transition-metal orbitals.

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