Emergence of the Chern structure using Sr${}_2$RuO${}_4$ nanofilms

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 external 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 $\theta =\pi \mathrm{/}6$ is determined by observing the topological magneto-electric effect in Sr${}_2$RuO${}_4$ nanofilms.