Possibility of Photoinduced Superconductivity

The possibility of interband electron pairing induced by the virtual exchange of quanta of two boson fields (photons and phonons) is theoretically examined. The system in question comprises two conduction bands which are, in general, separated by an energy gap $E_{\mathrm{bc}}$. Radiative transitions between states of these bands are assumed to be allowed. Through appropriate canonical transformations, effective interband electron-electron interaction terms are obtained which involve, respectively, virtual exchange of (i) one photon (one-boson process), and (ii) one photon and one phonon (two-boson process). These are found to be attractive under certain conditions. The one-photon process is, however, rendered inconsequential owing to the very small volume of momentum space spanned by "interaction quantum" (photon) exchanged. The two-boson process, on the other hand, does not suffer from the above momentum-space restriction. Moreover, this latter process contains terms linear in the photon and the phonon occupation-number densities, and the reduction in the matrix elements can be compensated by boosting the boson occupation-number densities artificially. Estimates show that the photon-occupation-number term will be significant for a value of $\frac{n_{{\lambda }_0}}{V}\sim {10}^{16}/{\mathrm{cm}}^3$, where $n_{{\lambda }_0}$ is the photon occupation number and $V$ is the volume. The corresponding phonon occupation-number density has to be of the order of ${10}^{20}$/${\mathrm{cm}}^3$. In that case, the interaction term is found to be anisotropic with respect to the direction of injected phonons. Expressions for the superconducting energy gaps at $T=0\mathrm{}°$K are derived by a Green's-function technique. The transition temperature for $\frac{n_{{\lambda }_0}}{V}\sim {10}^{17}/{\mathrm{cm}}^3$ is found to be of the order of ${10}^2$ °K.