The Bardeen, Cooper, and Schrieffer theory of superconductivity is extended to the case of high current densities by explicitly including in the phonon-induced electron-electron attraction the modification of the phonon spectrum in a moving coordinate system. This modification results from the Doppler effect. In materials having cross-sectional dimensions of the order of the penetration depth, it is shown that at current densities of the order of 10 9 amp/cm 2 the superconducting state is stable relative to the normal state, this holding both in superconducting metals and in metals ordinarily not considered superconducting at all. For this high-current state, it appears possible to obtain superconducting transition temperatures as high as room temperature. Means for achieving such an effect experimentally are discussed. making the approximation. As we shall see in the following section, however, the Doppler effect on the phonon spectrum is crucial to the very existence of the highcurrent range of superconductivity. Because of the Doppler effect, the phonon-induced attraction between electrons rises rapidly as the electronic drift velocity approaches the speed of sound. In the high-current region of superconductivity the effective energy gap may be several orders of magnitude larger than the gap in the low-current region. Thus it is not unreasonable to expect room-temperature superconductivity in the highcurrent range.The theory indicates that high-current superconductivity should occur not only in superconducting materials but also (even more strikingly) in metals such as copper which are ordinarily not superconductors at all.In Sec. Ill we will discuss some of the difficulties in actually getting high-current superconductivity experimentally. A particular experimental arrangement for achieving it will be proposed. The technological importance of the effect will be discussed briefly.
II. THEORYThe dc current density J-ne\ in a superconducting metal can be broken into two parts, a conduction current density J c = (ne/m)po and a diamagnetic current densityHere n is the density of superconducting electrons, v their mean velocity, m their effective mass, po their mean momentum, and A the vector potential, J<* represents that portion of the current resulting from magnetic interactions, whereas J c represents the current that would occur if there were no magnetic interactions or, more specifically, if the velocity of light c were set equal to infinity without changing the boundary conditions which specify the total current flowing through the superconductor. This means that the total current flowing across a cross-sectional area of the conductor must result entirely from J c ; the integral of J^ over the area vanishes. Jd is solenoidal (VXJ^O), whereas J c 1390