Conductance features of core-shell nanowires determined by the internal geometry

We consider electrons in tubular nanowires with prismatic geometry and infinite length. Such a model corresponds to a core-shell nanowire with an insulating core and a conductive shell. In a prismatic shell the lowest energy states are localized along the edges (corners) of the prism and are separated by a considerable energy gap from the states localized on the prism facets. The corner localization is robust in the presence of a magnetic field longitudinal to the wire. If the magnetic field is transversal to the wire the lowest states can be shifted to the lateral regions of the shell, relatively to the direction of the field. These localization effects should be observable in transport experiments on semiconductor core-shell nanowires, typically with hexagonal geometry. We show that the conductance of the prismatic structures considerably differs from the one of circular nanowires. The effects are observed for sufficiently thin hexagonal wires and become much more pronounced for square and triangular shells. To the best of our knowledge the internal geometry of such nanowires is not revealed in experimental studies. We show that with properly designed nanowires these localization effects may become an important resource of interesting phenomenology.