Mott transition

A transition between conducting and insulating behavior caused by strong interactions among particles, even when simple band theory predicts metallic conduction.

Hubbard model: A lattice model describing particles that hop between sites and interact through an on-site repulsion. It captures the competition between electron motion and repulsion that drives the transition.
Electron correlation: The dependence of an electron’s behavior on the positions and motions of other electrons. Correlated motion is the underlying source of the interaction-driven insulating state.
Vanadium dioxide: A compound that undergoes a sharp temperature-driven transition between insulating and metallic states. Its transition is a prominent case where structural change and electronic correlations are intertwined.
Band insulator: An insulator in which completely filled energy bands are separated from empty bands by an energy gap. Its insulating gap follows from band filling, unlike the correlation-driven gap of a Mott insulator.
Mott insulator: An insulating state in which interactions localize particles despite a partially filled electronic band. It is the insulating phase produced when repulsion suppresses charge motion.
Coulomb interaction: The electrostatic force between electrically charged particles. Its energy cost for neighboring electrons occupying the same site drives localization.
V2O3: A vanadium oxide whose pressure- and temperature-dependent phases include a paramagnetic metal and a Mott insulator. Its phase diagram established a canonical setting for studying correlated metal-insulator transitions.
Anderson localization: The loss of diffusive transport when disorder localizes wave functions in a system. It also suppresses conduction, but disorder rather than strong particle interactions is central.
Mott gap: An energy gap for adding or removing a charge in an interaction-driven insulator. The gap separates the insulating state from mobile charge excitations.
Hubbard U: The on-site interaction energy for two electrons occupying the same lattice site in the Hubbard model. Compared with bandwidth, it measures the strength of the local repulsion.

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