With recent technologies thin core-shell nanowires of 100 nm diameter or less, and length up to tens of µm, can be fabricated with semiconductors. Such a structure is made of a core of one material surrounded by a layer of another material, and can be seen as a radial version of the classical planar heterojunction. With an insulating core and a thin conductive shell one obtains a conductor with tubular geometry. In this presentation three types of electronic localization in tubular shells will be discussed, together with their physical consequences.
1. The primary radial localization has consequences in magnetotransport. When travelling along the tube the electrons perform loops which generate conductance oscillations of Aharonov-Bohm nature.
2. In a magnetic field perpendicular to the tube an angular localization develops along the directions lateral to the field, where so-called called snaking orbits are created. The electronic current flows along these regions leading now to Aharonov-Bohm-like oscillations along the longitudinal contour of the nanowire. Another consequence of this angular localization is the sign reversal of the electric current generated along the nanowire by a temperature bias.
3. Due to the original crystalline structure of the materials used for fabrication the cross section of bottom-up grown nanowires is usually polygonal, most often hexagonal. The electrons situated in a thin polygonal shell have the ground state localized in the corners, and separated by a gap from higher energy states localized on the sides. The size of this gap depends on the details of the shell geometry. A prismatic shell becomes an interesting arena for Majorana physics. It can host different Majorana states along each edge, with possible interactions, depending on the aspect ratio of the shell (thickness vs. radius), and on the sharpness of the corners.