The excitonic ground state of the half-filled Peierls insulator

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 2 Delta 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 Frohlich (1954) one-dimensional charge-density-wave state.