We discovered a fractional Chern structure in chiral superconducting Sr$_2$RuO$_4$ nanofilms by employing electric transport. By using Sr$_2$RuO$_4$ single crystals with nanoscale thickness, a fractional Hall conductance was observed without an exter
nal magnetic field. The Sr$_2$RuO$_4$ nanofilms enhanced the superconducting transition temperature to about 3 K. We found an anomalous induced voltage with temperature and thickness dependence, and the switching behavior of the induced voltage appeared when we applied a magnetic field. We suggest that there was fractional magnetic-field-induced electric polarization in the interlayer. These anomalous results are related to topological invariance. The fractional axion angle $theta=pi/6$ is determined by observing the topological magneto-electric effect in Sr$_2$RuO$_4$ nanofilms.
We observed an unconventional parity-violating vortex in single domain Sr2RuO4 single crystals using a transport measurement. The current-voltage characteristics of submicron Sr2RuO4 shows that the induced voltage has anomalous components which are e
ven function of the bias current. The results may suggest that the vortex itself has a helical internal structure characterized by a Hopf invariant (a topological invariant). We also discuss that the hydrodynamics of such a helical vortex causes the parity violation to retain the topological invariant.
