Topological Invariant Explanation of the Quantum Hall Effect (TKNN)

Thouless, Kohmoto, Nightingale & den Nijs's 1982 discovery that the integer quantum Hall effect's quantized conductance is a topological invariant (a Chern number) of the electronic band structure -- a more general explanation than Laughlin's 1981 gauge argument, and the direct theoretical ancestor of the entire topological-phases-of-matter field (topological insulators, Weyl semimetals, QAHE) that followed decades later. Per the nearest-parent-only rule, linked here to Integer QHE (the phenomenon it explains) rather than to every downstream topological-matter node it influenced.