Emergence of an excitonic collective mode in the dilute electron gas

In the early 1950s, Bohm and Pines (BP) developed the random-phase approximation (RPA) theory and revealed the plasmon as an emergent collective mode in metals. In this paper, for the first time ever since the original BP theory, a novel collective mode is predicted to emerge in the dilute electron liquid. The electronic compressibility of this mode is negative and thus dielectric catastrophe appears, predicted by a theory that goes far beyond RPA and fully satisfies various sum rules, constraints, and asymptotic behavior. While the plasmon occurs by the coherent excitations of mutually uncorrelated electrons and holes, the new mode is associated with the excitations of a large collection of excitons (or tightly bound electron-hole pairs). Mathematically, this excitonic collective mode is intimately connected with a newly discovered singularity in the dielectric function in the electron liquid. This collective mode should add a new dimension to plasmonics in nanotechnology in the future.