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A Mott transition is a change between a conducting state and a Mott insulator, driven by the competition between electron motion and electron repulsion. A partially filled energy band need not conduct if repulsion makes moving an electron onto an already occupied site too costly.

The half-filled Hubbard model illustrates the mechanism: hopping lowers the kinetic energy, whereas on-site repulsion $U$ penalizes double occupation. Increasing $U$ relative to the energy-band width can suppress charge motion and open a gap for charge excitations. Changing pressure, composition or carrier concentration can alter that competition, although actual materials may also change their crystal structure or magnetic order. This interaction mechanism differs from a band insulator with filled bands and from disorder-driven Anderson localization.

The energy-band widths are the difference between their extrema:For the separated bands, the top of the $s$ band and bottom of the $p$ band are both at $k=\pi /a$. HenceIt is a direct band gap at the zone boundary, because both limiting states have the same wavevector. This result uses the opposite signs of the $s$ and axial-$p$ hoppings.