Excitation spectrum and electromagnetic properties of the electron-exciton bound states in molecular crystals

A self-consistent approach is used to study the excitation spectrum due to the coherent electron-exciton pairing for a two-level system of a molecular crystal. It is shown that the interaction between an excited electron and a Frenkel exciton, which are located at adjacent lattice sites in the crystal, leads to the formation of a bound state provided that certain conditions are satisfied. The excitation spectrum is found to be of the superconductivity type and the electron-exciton quasiparticle moves through the crystal with definite energy and wavevector. The gap function due to the electron-exciton pairing is calculated at zero temperature and an expression for the ground-state energy is derived. Then the electromagnetic properties of the electron-exciton bound states are discussed. An expression for the dielectric function is obtained describing the interaction between the transverse photons and the two charged quasiparticles which arise from the electron-exciton pairing. In the presence of electron-exciton pairing, the paramagnetic current consists of two terms arising from the two frequency modes, which in the long-wavelength limit cancel each other to the order of Δ/E_νO, where Δ is the gap function due to the electron-exciton pairing and E_νO is the energy difference between the excited and ground state. Thus for Δ ⪡ E_νO the diamagnetic current in the long-wavelength limit is the same as in London's theory indicating the existence of the Meissner effect. In the absence of pairing the diamagnetic current vanishes.