Cycloid crystals by topology change

A cycloid, formerly known as a roulette, is a curve arising from a point on a circumference that rolls on its plane over a fixed straight line, and the cycloid shape is observed in many natural objects formed under a constraint. Here we report the discovery of cycloid-shaped crystals of TaSe3 obtained via the “topology-change surgery” of thin ring-shaped crystals. We cut the ring-shaped crystals with a focused ion beam. After being cut, they formed a cycloidal shape similar to Cyclotron trajectories of electrons under magnetic and electric fields. We conclude that the inhomogeneous curvature distribution minimizes the bending energy and shear modulation, which corresponds to our shear-less model.

► The surgery method changes the topological constraint of the ring-shaped crystals of TaSe3.
► We found that the curves of the thin ring-shaped crystals can be transformed from circle to cycloid or trochoid.
► Role of the shear modulation for the curvature distributions is discussed.