Cooper-pair mass

Abstract

The Cooper-pair mass m* is defined by use of the gauge-invariant momentum, p*=m*v=[(h/2π)∇φ-/B (e*/c)A], where φ is the phase of the macroscopically occupied wave function of Cooper pairs of charge e* (twice the electron charge), A is the total magnetic vector potential, and we have taken the limit of v≪c. We point out that for a general class of experiments in which the superconductor is in steady-state motion with respect to the laboratory (including uniform rotation), the physically observable Cooper-pair mass m’ is measurable, where m’=m*+e*〈Φ〉/c2 and 〈Φ〉 is the expectation value of the total microscopic electrostatic potential in the bulk metal averaged over the single-electron states that contribute to the superconducting pair wave function. To lowest order m’=m*=2me, and to first order m*c2=μ*-e*〈Φ〉 and m’c2=μ*, where μ* is the electrochemical potential (including the rest mass 2mec2 and the work function W). For niobium the intrinsic mass is m*/2me≊1.000 18, and the observable mass for experiments is m’/2me≊0.999 992.

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