  We revisit the supercurrent generation mechanism for superconductors whose
superconducting transition temperature are explained by the BCS theory,
motivated by the reexamination of the ac Josephson effect [J. Supercond. Nov.
Magn. (2015) 28:61] that indicates the electromagnetic vector potential ${\bf
A}^{\rm em}$ couples to each electron in the pairing electrons, separately, as
$e{\bf A}^{\rm em}$, not together as $2e{\bf A}^{\rm em}$. To satisfy the above
finding, we argue that the origin of the supercurrent generation is the
emergence of Dirac strings with $\pi$ flux inside. It appears if the Rashba
spin-orbit interaction is added to the BCS model due to its stabilization of
the spin-twisting itinerant motion of electrons. The $\pi$-flux Dirac string
generates the cyclotron motion without external magnetic field, and produces
topologically protected loop current. This can be also attributed to the
emergence of the $U(1)$ instanton of the Berry connection ${\bf A}^{\rm fic}=-{
\hbar \over {2e}} \nabla \chi$, ${\bf \varphi}^{\rm fic}={ \hbar \over {2e}}
\partial_t \chi$, where $\chi$ is an angular variable of period $2\pi$. The
phase of the macroscopic wave function for the Ginzburg-Landau theory or the
phase of the pair potential of the Bogoliubov-de Gennes equations is identified
as $\chi$. If it is treated as a phenomenological parameter, the
Ginzburg-Landau theory or the Bogoliubov-de Gennes equations can be used
without modification. However, the new origin requires the Rashba interaction
for the occurrence of superconductivity. This may explain the fact that ideal
metals like sodium does not show superconductivity since the screening of the
electric field is efficient in such materials, suppressing the internal
electric field too weak to occur superconductivity.
