We point out that the half-filled Peierls insulator, celebrated for its soliton excitations and
its application to trans(polyacetylene), is an excitonic insulator in which collectively bound
electron–hole pair excitations (excitons) are mixed into the ground state. Unlike the bound
electron pairs of the Bardeen–Cooper–Schrieffer (BCS) superconductor, however, the excitonic
pairs can be photoionized leading to the direct observation of the excitonic energy gap
2Δ
in the optical conductivity. A deeper understanding is provided of the discovery of Kuper in
1955 of a BCS-like gap equation describing the thermodynamic properties of the Fröhlich
(1954) one-dimensional charge-density-wave state.