Designing electron spin textures and spin interferometers by shape deformations

We demonstrate that the spin orientation of an electron propagating in a one-dimensional nanostructure with Rashba spin-orbit (SO) coupling can be manipulated on demand by changing the geometry of the nanosystem. Shape deformations that result in a nonuniform curvature give rise to complex three-dimensional spin textures in space. We employ the paradigmatic example of an elliptically deformed quantum ring to unveil the way to get an all-geometrical and all-electrical control of the spin orientation. The resulting spin textures exhibit a tunable topological character with windings around the radial and the out-of-plane directions. We show that these topologically nontrivial spin patterns affect the spin interference effect in the deformed ring, thereby resulting in different geometry-driven ballistic electronic transport behaviors. Our results establish a deep connection between electronic spin textures, spin transport, and the nanoscale shape of the system.