  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.
