band overlap
/ band OH-vur-lap /
Picture two staircases side by side, one ending and the next beginning. Normally the top of one sits below the bottom of the next, leaving a clear gap to jump. But if the staircases are tilted so that the top of the lower one reaches higher than the bottom of the upper one, their steps share the same heights for a stretch. When energy bands do this, they overlap.
Band overlap happens when the top of one energy band rises higher than the bottom of the next band, so the two bands share a range of energies instead of being separated by a gap. When this occurs, electrons that would otherwise have exactly filled the lower band spill over to partly fill the upper one too, leaving both bands partly full. The result is empty states sitting right alongside occupied ones — the very condition for conduction.
Band overlap matters because it is the loophole that turns a material which counting alone says should be an insulator into a metal. Elements like magnesium, calcium, and zinc have just enough electrons to fill a band exactly, yet conduct because their bands overlap — and the overlap is large enough that they end up being perfectly good metals, conducting on the same order as copper. The label semimetal is reserved for a different case — materials like bismuth, antimony, arsenic, and graphite, whose band overlap is so tiny that they have very few carriers and conduct far more weakly than a metal like copper whose top band is generously half-empty.
Magnesium has two outer electrons per atom — exactly enough, you would think, to fill its valence band and make an insulator. Instead, magnesium's bands overlap: electrons spill into the next band, both bands end up partly filled, and magnesium turns out to be a perfectly good metal that conducts electricity well.
Overlapping bands let magnesium conduct, though simple counting predicts an insulator.
Band overlap is the opposite situation to a band gap: a gap separates two bands with forbidden energies between them, while overlap means the two bands share energies, which is exactly why a would-be insulator can end up conducting.