  Persistent current generation by small polarons embedded in a spin-density
wave background in a two dimensional lattice is theoretically studied. When the
embedded small polarons become cores of merons and antimerons (vortices in spin
configuration with winding numbers +1 and -1, respectively), a spin Berry phase
arises from the spiral spin texture of the merons and antimerons, and generates
a spin current around the polarons. Electric current is, however, absent due to
the exact cancellation of the up- and down-spin electron currents. By addition
of an imaginary magnetic flux that negates the fictitious magnetic flux from
the spin Berry phase, the state with merons and antimerons is stabilized and
non-zero electric current appears; this imaginary flux becomes a real one when
side-by-side bipolaronic cores of merons and antimerons are formed, where the
real flux arises spontaneously from the wave function for the motion of the
system as a whole; thus, the bipolarons serve as pumps for the persistent
electric current. It is also shown that a Nernst signal stems from thermal
diffusion of the bipolarons. Implications of the present results to anomalous
properties of cuprate superconductors, including the enhanced Nernst signal,
Drude peak, and Fermi arc are also discussed. The present result suggests the
appearance of the phase variable or ``Nambu-Goldstone'' mode for the
superconductivity without the breakdown of the global U(1) gauge invariance in
the cuprates.
