Superconductivity originating from a repulsive potential: Proposal of a new exciton mechanism of high-Tcsuperconductivity in the dilute electron gas

We investigate the possibility of superconductivity and estimate the transition temperature $T_c$ in a system in which the bare electron-electron interaction $V\left(q\right)\mathrm{}$ is arbitrary but basically repulsive. We employ the recently developed variational method which is believed to be the best one for the purpose at present. Through this study, we consider a concept of the Cooper pair originating not from an attractive but rather a repulsive bare potential. We find a special form for $V\left(q\right)\mathrm{}$ to obtain $T_c$ over 200 K in the dilute electron-gas system. We discuss the band structure near the Fermi surface to produce such $V\left(q\right)\text{'}\mathrm{s}$ and propose a new exciton mechanism.