We investigate the nature of the superconducting state in curvednanostructures with Rashba spin-orbit coupling (RSOC). In bent nanostructureswith inhomogeneous curvature we find a local enhancement or suppression of thesuperconducting order parameter, with the effect that can be tailored by tuningeither the RSOC strength or the carrier density. Apart from the localsuperconducting spin-singlet amplitude control, the geometric curvaturegenerates non-trivial textures of the spin-triplet pairs through a spatialvariation of the d-vector. By employing the representative case of anelliptically deformed quantum ring, we demonstrate that the amplitude of thed-vector strongly depends on the strength of the local curvature and itgenerally exhibits a three-dimensional profile whose winding is tied to that ofthe single electron spin in the normal state. Our findings unveil novel pathsto manipulate the quantum structure of the superconducting state in RSOCnanostructures through their geometry.
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