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Majorana states in prismatic core-shell nanowires
We consider core-shell nanowires with conductive shell and insulating core,
and with polygonal cross section. We investigate the implications of this
geometry on Majorana states expected in the presence of proximity-induced
superconductivity and an external magnetic field. A typical prismatic nanowire
has a hexagonal profile, but square and triangular shapes can also be obtained.
The low-energy states are localized at the corners of the cross section, i.e.
along the prism edges, and are separated by a gap from higher energy states
localized on the sides. The corner localization depends on the details of the
shell geometry, i.e. thickness, diameter, and sharpness of the corners. We
study systematically the low-energy spectrum of prismatic shells using
numerical methods and derive the topological phase diagram as a function of
magnetic field and chemical potential for triangular, square, and hexagonal
geometries. A strong corner localization enhances the stability of Majorana
modes to various perturbations, including the orbital effect of the magnetic
field, whereas a weaker localization favorizes orbital effects and reduces the
critical magnetic field. The prismatic geometry allows the Majorana zero-energy
modes to be accompanied by low-energy states, which we call pseudo Majorana,
and which converge to real Majoranas in the limit of small shell thickness. We
include the Rashba spin-orbit coupling in a phenomenological manner, assuming a
radial electric field across the shell.Comment: 14 pages, 16 figures, accepted for publication in Phys. Rev.
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