Electrons in core-shell nanowires and the possibilities of hosting Majorana states



        I will present a theoretical study of electrons confined in core-shell nanowires of different material and geometry. These radial heterojunctions have attracted considerable attention due to their unique and controllable properties which render them possible building blocks of many quantum nanodevices. In this presentation I will study how cross-section geometry and material parameters determine the low-energy levels and the corresponding localization of electrons confined in prismatic shells. In particular, I will specify conditions allowing to obtain a well-separated group of corner states and I will study conditions allowing to host multiple Majorana states within a single tubular wire.

     Core-shell nanowires are usually grown vertically and, due to the crystallographic structure, have polygonal cross sections, most commonly hexagonal, but triangular, and rectangular systems have also been obtained. Moreover, recently structures combining two polygons in one cross section, such as triangular shells grown on hexagonal cores, became technologically feasible [1].  Appropriate band alignment or core etching allows to obtain conductive shells.   The polygonal cross section of such shells induces non-uniform electron localization along the wire circumference. In particular, in the corner areas effective quantum wells are formed which attract low energy electrons. This results in electron accumulation in corner areas and formation of conductive channels along the sharp edges, i.e. one structure may contain a few 1D wires.  The corner states can be energetically separated from higher, corner or side states, by a gap which may considerably exceed the room-temperature energy, and thus such states provide a subspace which is robust against many perturbations [2]. Since each edge can act as a quantum wire it may also host Majorana states, in particular, a single prismatic tube may contain multiple Majorana states [3, 4]. The electron localization is very sensitive to imperfections which are inevitably present in realistic structures. If one facet of the shell is considerably thicker than the other ones, then the corner localization is destroyed and the ground state is localized on the thickest facet which becomes the only conductive channel in the structure [5]. Spin-orbit interaction has recently been studied in prismatic wires [6], but not much is known about its role in prismatic tubular systems. In this presentation I will show how spin-orbit interaction affects the energies of electrons confined in the outer regions of core-shell wires.

1. D.J.O. Göransson, et al., Appl. Phys. Lett. 114, 053108 (2019).
2. A. Sitek, et al.,  Phys. Rev. B 91, 235429 (2015).
3. A. Manolescu, A. Sitek, et al.,  Phys. Rev. B 96, 125435 (2017).
4. T. D. Stanescu, A. Sitek, and A. Manolescu, Beilstein J. Nanotechnol. 9, 1512 (2018).
5. M.M. Sonner, A. Sitek, et al., Nano Lett. 19, 3336 (2019).
6. P. Wójcik et al., Phys. Rev. B  97, 165401 (2018); Phys. Rev. B  103, 085434 (2021).