We report the prediction and observation of supra-binary ferroelectricity in a ferroelectric nanowire (FNW) covered with a semi-cylindrical gate that provides an anisotropic electric field in the FNW. There are gate-voltage-driven transitions between four polarization phases in FNWs cross section, dubbed axial-up, axial-down, radial-in and radial-out. They are determined by the interplay between the topological depolarization energy and the free energy induced by an anisotropic external electric field, in clear distinction from the conventional film-based binary ferroelectricity. When the FNW is mounted on a biased graphene nanoribbon (GNR), these transitions induce exotic current-voltage hysteresis in the FNW-GNR transistor. Our discovery suggests new operating mechanisms of ferroelectric devices. In particular, it enables intrinsic multi-bit information manipulation in parallel to the binary manipulation employed in data storage devices.
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