Polarization vortices that typically form in ferroelectric nanostructures are fundamental polar topological structures characterized by a curling polarization around a stable core. The control of vortex chirality by conventional fields including homogeneous electric field is a key to the utilization of vortices in technological applications. However, an effective control of the vortex chirality by such an electric field remains elusive since the toroidal moment of ferroelectric vortex is conjugated to a curled electric field rather than the homogeneous electric field. Here we demonstrate the control of vortex chirality by homogeneous electric field in free-standing nanodots with rationally designed nanostructures. The nanodots are designed by including a notch or an antinotch in the rectangular structure of nanodots. The results show that the chirality of polarization vortex is deterministically switched by a homogeneous electric field through the control of depolarization distribution by designed structures. The evolution path under homogeneous electric field in antinotched nanodot takes place in the opposite direction in comparison with that in notched nanodot. We further demonstrate that the designed nanostructures break the symmetry of electrostatic field in the ferroelectric systems, where the depolarization field concentrates at the notch but scatters at the antinotch. Such a symmetry breaking of electrostatic field results in the opposite evolution paths in the notched and antinotched nanodots under homogeneous electric field and provides the fundamental reason that allows such control. The present study suggests a new route on the practical control of the vortex domain pattern in ferroelectric nanostructures by homogeneous electric field.
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