  We show that the Rashba spin-orbit interaction causes spin-twisting itinerant
motion of electrons in metals and realizes the quantized cyclotron motion of
conduction electrons without an external magnetic field. From the view point of
the Berry connection, the cause of this {quantized} motion is the appearance of
a non-trivial Berry connection ${\bf A}^{\rm fic}=-{\hbar \over {2e}}\nabla
\chi$ ($\chi$ is an angular variable with period $2\pi$ that generates $\pi$
flux (in the units of $\hbar=1, e=1,c=1$) inside the nodal singularities of the
wave function (a "Dirac string") along the centers of spin-twisting.
  Since it has been shown in our previous work[Ref.1]that the collective mode
of $\nabla \chi$ is stabilized by the electron-pairing and generates
supercurrent, the $\pi$-flux Dirac string created by the spin-twisting
itinerant motion will be stabilized by the electron-pairing and produce
supercurrent.
