Core–shell nanowires are radial heterostructures consisting of a core nanowire covered by a layer of a different material. These structures have attracted considerable attention due to their unique and tunable properties, which offer promising applications in quantum technologies. The cores are typically grown vertically, and their crystallographic structure often results in polygonal cross-sections, most commonly hexagonal. The shells are generally deposited onto the cores, following their geometry [1]. However, structures combining triangular and hexagonal shapes have also been demonstrated [2,3]. Moreover, by employing appropriate band alignment, it is possible to shift electrons toward the outer regions, causing the shells to act as conductive tubes.
We present a theoretical study of electrons confined in prismatic tubular wires, which correspond to the outer regions of core–shell nanowires. We investigate how the cross-sectional geometry influences the low-energy states of electrons and their spatial distribution around the shell. Our findings show that triangular shells can generate three independent quantum wires in the low-energy regime, while at higher energies they behave as coupled wires. Furthermore, the lowest-energy states are localized along the sharp edges of the shell and are energetically separated from the states localized on the facets by energy gaps that can be large, possibly even exceeding the room-temperature energy [4].
In addition to quantum localization, we incorporate into our model the spin–orbit interaction arising from the band discontinuity at the core–shell interface. This interaction affects the energy states of hexagonal and triangular shells in qualitatively different ways, splitting the fourfold-degenerate levels into two or three distinct states. In the case of narrow triangular structures, the states localized along the edges and on the facets are also affected differently: the lower-energy states form shifted parabolas, while the higher-energy states split into four states. In the presence of an external electric field, the corner states exhibit behavior typical of non-interacting wires, whereas the higher-energy states behave as coupled systems [5].
1. M. M. Sonner, A. Sitek, et al., Nano Lett. 19, 3336 (2019).
2. D. J. O. Göransson, et al., Appl. Phys. Lett. 114, 053108 (2019).
3. X. Yuan, et al., Adv. Funct. Mater. 25, 5300 (2015).
4. A. Sitek, et al., Phys. Rev. B 91, 235429 (2015).
5. A. Sitek, et al., Phys. Rev. B 112, 115433 (2025).
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