Spin-Orbital Textures and Interferometers by Nanoscale Geometric Design of Quantum Rings with Orbital Rashba Coupling

Abstract: We derive an effective continuum model for describing the propagation of electrons in ballistic one-dimensional curved nanostructure which are marked by a strong interplay of spin-orbital degrees of freedom due to local electronic states with $d-$orbital symmetry, atomic spin-orbit and orbital Rashba couplings. We demonstrate how a planar inhomogeneous spatial curvature of the nanochannel can generate both spin and orbital textures represented through loops on the corresponding Bloch spheres. In particular, we employ the paradigmatic case of an elliptically shaped quantum ring to investigate the role of geometry in steering the electron transport at low energy. We find that in this regime spin and orbital textures exhibit equal windings around the radial or out-of-plane directions. Remarkably, the spin and orbital windings can be not only tuned through a modification of the nanoscale shape, as for the spin Rashba effect, but also via a change in the electron density by electrical gating. We show that the presence of textures is related to patterns in the geometric Aharonov-Anandan phase acquired in a cycle within the quantum ring. Furthermore, differently from the single band Rashba-coupled nanoring, a manipulation of the conductance can be achieved by electron density variation and, indirectly, through changes of the strength of the inversion asymmetric interactions.