A correction to Schafroth's superconductivity solution of an ideal charged boson system

Abstract

The Schafroth superconductivity solution of an ideal gas of charged bosons (with an external uniform background charge density so that the whole system is electrically neutral) gives for the critical magnetic field H c ( T) = [2 eλ L 2( T)] −1, in units h = c = 1, where T is the temperature (assumed to be less than T c ), λ L ( T) is the London length and e the boson charge. We show that the formula is invalid because the electrostatic exchange energy E ex between bosons has been completely left out in the Schafroth solution. Based on the Schafroth solution, E ex is found to be + ∞ in the normal phase, but 0 in the condensed phase (at T = 0). Of course, the correct solution has to give a finite E ex. At low density the ideal charged boson system turns out not to be a superconductor, but becomes a type II superconductor at high density, with a critical field H c much larger than the Schafroth result.