Cooper-pair mass

The Cooper-pair mass $m^{\mathrm{*}}$ is defined by use of the gauge-invariant momentum, ${\mathrm{p}}^{\mathrm{*}}$=$m^{\mathrm{*}}$v=[(h/2π)∇φ-/B ($e^{*}$/c)A], where φ is the phase of the macroscopically occupied wave function of Cooper pairs of charge $e^{\mathrm{*}}$ (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’=$m^{\mathrm{*}}$+$e^{\mathrm{*}}$〈Φ〉/$c^2$ 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’=$m^{\mathrm{*}}$=2$m_e$, and to first order $m^{\mathrm{*}}$ $c^2$=${\mu }^{\mathrm{*}}$-$e^{\mathrm{*}}$〈Φ〉 and m’ $c^2$=${\mu }^{\mathrm{*}}$, where ${\mu }^{\mathrm{*}}$ is the electrochemical potential (including the rest mass 2$m_e$ $c^2$ and the work function W). For niobium the intrinsic mass is $m^{\mathrm{*}}$/2$m_e$≊1.000 18, and the observable mass for experiments is m’/2$m_e$≊0.999 992.