Mott insulator
/ MOT IN-suh-lay-tor /
Imagine a long row of single-occupancy parking spaces, with exactly one car per space. By the usual rules of traffic, cars should be free to inch forward and the whole line should flow. But suppose every driver flatly refuses to let a second car share their space — even for an instant. Then nobody can move, because moving forward means briefly doubling up. The cars are jammed by their own stubbornness, not by any wall.
Replace cars with electrons and spaces with atoms, and you have a Mott insulator. Ordinary band theory would call this material a metal: it has a half-filled band, so electrons ought to flow and conduct. But the electrons repel one another so strongly that putting two on the same atom costs too much energy. To conduct, an electron would have to hop onto an already-occupied atom, and it can't afford to — so the material refuses to conduct at all.
It matters because it shows that interactions, not just band-filling, decide whether a material conducts — a fact the entire 20th-century band theory of metals had quietly assumed away. The honest caveat: a Mott insulator looks deceptively like an ordinary insulator from the outside, but it is a different beast, and squeezing it or doping it can turn it into a metal or even a superconductor.
Nickel oxide and many other transition-metal oxides are textbook Mott insulators. By simple band counting they should be good metals, yet they are stubborn electrical insulators — a contradiction that, once Nevill Mott explained it through electron repulsion, opened the whole field of strongly correlated materials.
Nickel oxide should conduct by band counting, yet electron repulsion makes it an insulator.
Don't confuse a Mott insulator with an ordinary band insulator. A band insulator can't conduct because its bands are completely full or empty; a Mott insulator has a partly filled band and 'should' conduct, but mutual repulsion freezes the electrons in place. The cause is interaction, not geometry.