High-Current Superconductivity?

The superconducting-gap equation has been re-examined for samples of cross section smaller than the penetration depth in which current is flowing. The effects of retardation of the electron-phonon interaction have been included by means of Green's-function techniques. The enhancement of the gap function due to Doppler shifting downward of the phonon frequencies, suggested by Parmenter five years ago, is again found. However, using the best current values for the metallic parameters involved, we find the magnitude of the effect too small to give the anticipated high-current, high-transition-temperature superconductors. We estimate that electron-phonon coupling constants $N\left(O\right)\mathrm{}{V}_0\gtrsim 0.77$ (almost double any observed in metals) and zero-current superconducting transition temperatures of the order of 50-100°K would be required to produce a stable high-current superconducting state.