Excitons in Metals: Infinite Hole Mass

TLDR

The study calculates optical conductivity for interband transitions between a flat valence band and a parabolic conduction band, with the conduction band filled to the Fermi energy and assuming a static short‑range attractive electron‑hole interaction. The attractive electron‑hole interaction produces a power‑law divergence in the conductivity at the interband threshold, and for an infinite hole mass the exciton binding energy vanishes.

Abstract

The optical conductivity is evaluated for interband transitions between a flat valence band and a parabolic conduction band. The conduction band is filled with electrons to a Fermi energy ${\ensuremath{\mu}}_{F}$. The conductivity is calculated assuming that the electron-hole interaction is attractive, static, and short range. The final-state interactions between the electron and hole cause a divergence in the conductivity at the interband threshold. This divergence appears to go as a power law. For this case of an infinite hole mass, the exciton binding energy vanishes, since the singularity in the scattering amplitude occurs just at threshold.